ELEMENTS 


OF 


NATURAL  PHILOSOPHY, 


A    TEXT-BOOK 


FOR    HIGH    SCHOOLS    AND    ACADEMIES, 


BY 

ELROY   M.   AVERY,    Pn.M., 


PRINCIPAL    OF    THE    EAS  T    HI  G  I!    SCHOOL,    CLEVELAND,    OHIO 


ILLUSTRATED  BY  NEARLY  400  WOOD  ENGRAVINGS. 


NEW     YORK-. 

SHELDON  &  COMPANY, 

No.   8    MURRAY    STREET. 

1881. 


PROF.  AVERY'S 
NATURAL   SCIENCE   SERIES. 


ISt. 

THE    ELEMENTS   OF    NATURAL    PHILOSOPHY. 

2nd. 
TEACHER'S    HAND    BOOK. 

TO   ACCOMPANY  AVERY'S  NATURAL   PHILOSOPHY;    CONTAINING 
SOLUTIONS   OF    PROBLEMS,    PRACTICAL   SUGGESTIONS,    &c. 

3rd. 
AVERY'S   ELEMENTS    OF   CHEMISTRY. 


Copyright,  1878,  by  Sheldon  &  Co. 


Electrotypcd  by  SMITH  &  MoDouo.u,,  82  Beck:nan  Street,  New  York. 


ill 

I  '£  2    o 
2  g  §  S 

i:     -      / 


CHAPTER    I. 

THEDOMAIH     OF     PHYSICS. 

PAGE 

SECTION  I,— The  Domain  of  Physics 1 

"       II.— The  Properties  of  Matter C 

"     III.— The  Three  Conditions  of  Matter 21 

CHARTER     II. 
D  Y  X  A  M  I  C  S  . 

SECTION  I.— Force  and  Motion 25 

' "       II. — Gravitation 46 

"     III.— Falling  Bodies 57 

"      IV.— The  Pendulum 09 

"       V.— Energy 76 

CHAPTER    III. 

SIMPLE     MACHINES. 

SECTION  I.  — Principles  of  Machinery  ;  the  Lever 86 

"       II.— The  Wheel  and  Axle  ;  Wheel- work  97 

"     III.— The  Pulley  ;  the  Inclined  Plane 103 

"      IV. — The  Wedge,    Screw,   Compound    Machines    and 

Friction 109 

CHAPTER    IV. 

LIQUIDS. 

SECTION  I. — Hydrostatics 116 

"       II. — Liquid  Equilibrium  ;  Capillarity ;  Buoyancy 128 

"     III.— Specific  Gravity 135 

"     IV,— Hydrokinetics 145 


IV  CONTENTS. 

CHAPTER    Y. 

PNEUMATICS. 

PAGE 

SECTION'  I. — The  Atmosphere  and  Atmospheric  Pressure 156 

"       II. — The  Relation  of  Tension  and  Volume  to  Pressure.  163 
"     III. — Air,  Forcing  and  Lifting  Pumps  ;  the  Siphon. ...  168 

CHAPTER    VI. 

MAGNETISM     AND     ELECTRICITY. 

SECTION  I. — Magnets 1 84 

"       II.— Frictional  Electricity 197 

"     ill. — Electric  Condensers,  Lightning  and  Experiments.  215 

"     IV.— Voltaic,  Dynamo-  and  Thermo-Electricity 237 

CHAPTER    VII. 

SOUND. 

SECTION  I. — Nature,  Refraction  and  Reflection  of  Sound 267 

rt       II. — Composition  of  Sound  Waves  ;    Musical  Instru- 
ments     283 

CHAPTER    VIII. 

HEAT. 

SECTION  I. — Temperature,  Thermometers,  Expansion 305 

"       II. — Liquefaction,  Vaporization,  Distillation 317 

"     III.— Latent  and  Specific  Heat 329 

"     IV.— Modes  of  Diffusing  Heat 343 

*'      V.— Thermodynamics 355 

CHAPTER    IX. 

LIGHT. 

SECTION  I.— Nature,  Velocity  and  Intensity  of  Light 368 

"       II.— Reflection  of  Light 378 

"     III.— Refraction  of  Light 395 

"     IV.— Chromatics  and  Spectra 409 

'*       V. — Optical  Instruments  and  Polarization   422 

CONCLUSION  ;   ENERGY 434 

APPENDICES 442 

INDEX , ; , 450 


TO     THE     TEACHER 


IN  this  book  will  be  found  an  unusual  number  of  prob 
lems.  It  is  not  intended  that  each  member  of  each 
class  shall  work  all  of  the  problems.  It  is  hoped  that 
they  are  sufficiently  numerous  and  varied  to  enable  you 
to  select  what  you  need  for  your  particular  class.  No 
author  can  make  a  comfortable  Procrustean  bedstead. 

You  would  do  well  to  secure,  in  the  fall  of  the  year,  a 
supply  of  the  pith  of  elder  or  sunflower  stalk,  and  several 
full-blown  thistle-heads,  that  they  may  be  well  dried  and 
ready  for  experiments  in  electricity  during  the  dry,  cold 
weather  of  winter. 

The  author  would  be  glad  to  receive  any  suggestions 
from  any  of  his  fellow-teachers  who  may  use  this  book,  or 
to  answer  any  inquiries  concerning  the  study  or  apparatus. 

Most  of  the  apparatus  mentioned  in  this  book  may 
be  obtained  from  E.  S.  RITCHIE  &  SONS,  Boston,  or  of 
JAMES  W.  QUEEK  &  Co.,  Philadelphia. 

The  author  has  prepared  a  Teacher's  Hand-Book  to 
accompany  this  volume,  with  answers  to  the  problems, 
and  much  additional  matter  of  interest  to  teachers  of 
Natural  Philosophy. 


TO    THE    PUPIL. 


EECENT  careful  and  extended  examination  shows 
-'  that  diseases  of  the  eye,  such  as  near-sight,  are 
lamentably  frequent  among  school-children.  Your  eye- 
sight is  worth  more  to  you  than  any  information  you  are 
likely  to  gain  from  this  book,  however  valuable  that  may 
be.  You  are  therefore  earnestly  cautioned: 

1.  To  be  sure,  in  studying  this  or  any  other  book,  that 
you  have  sufficient  light. 

2.  That  you  do  not  allow  direct  rays  of  light  to  fall 
upon  your  eyes,  and  that  you  avoid  the  angle  of  reflection. 

3.  That  you  avoid  a  stooping  position  and  a  forward 
inclination  of  the  head.     Do  not  read  with  the  book  in 
your  lap.    The  distance  of  the  eye  from  the  page  should 
be  not  less  than  twelve  inches  (30  cm.)  nor  more  than 
eighteen  inches  (45  cm.)     Hold  the  book  tip. 

4.  That  you  sit    erect  when  you  write.      The    light 
should  be  received  over  your  left  shoulder. 

5.  Especially,  that  you  avoid,  as  much  as  possible,  books 
and  papers  poorly  printed  or  printed  in  small  type. 

6.  That  you  cleanse  the  eyes  with  pure  soft    water 
morning  and  night,  and  avoid  overtaxing  them   in  any 
way. 


THE    DOMAIN    OF    PHYSICS.— THE   PROPERTIES  OF 

MATTER. -THE    THREE    CONDITIONS 

OF    MATTER. 


ECTfON  I, 


THE    DOMAIN    OF    PHYSICS,    OR    NATURAL 
PHILOSOPHY. 

Introductory. — On  the  page  opposite,  you  hare  an 
outline  map  of  the  wide  realm  of  human  knowledge.  As 
from  a  mountain  top,  you  look  upon  the  plain  below,  and 
clearly  see  the  position  of  each  province,  and  its  relation 
to  its  neighbors.  Through  some  of  these  provinces  you 
may  have  passed,  and  with  them  have  become  more  or 
less  familiar.  From  the  whole  number  we  now  select  one 
that  promises  enough  of  interest  and  profit  to  justify  the 
time  and  effort  of  careful  study.  Not  satisfied  with  the 
cursory  glance,  we  seek  more  definite  information.  For 
this,  we  must  leave  the  peak  and  enter  the  plain;  for 
though  distance  may  lend  an  enchantment,  it  also  begets  a 
dimness  fatal  to  our  purpose. 

1.  What  is  Science  7  —  Science  is  classified 
knowledge. 

A  person  may  have  lived  for  years  among  plants,  have 
acquired  a  Vast  store  of  information  concerning  them, 


2  THE  DOMAIN  OF  PHYSICS. 

know  that  this  one  grows  only  in  wet  ground,  that  another 
is  valuable  for  such  and  such  an  end,  and  that  a  third 
has  certain  form,  size,  and  color.  This  general  informa- 
tion may  be  valuable,  but  it  is  only  when  the  facts  are 
classified,  and  the  plants  grouped  into  their  respective 
orders,  genera  and  species,  that  the  knowledge  becomes 
entitled  to  the  name  of  botany,  a  science. 

2.  What  is  Matter? — Matter  is  anything  that 
occupies  space  or  "  takes  up  room." 

There  are  many  realities  that  are  not  forms  of  matter. 
Mind,  truth,  and  hope  do  not  occupy  space ;  the  earth  and 
the  rain-drop  do. 

3.  Divisions  of  Matter. — Matter  may  be  con- 
sidered as  existing  in  masses,  molecules,  and  atoms. 

A  clear  apprehension  of  the  meaning  of  these  terms 
is  essential  to  a  full  understanding  of  the  definition  of 
Physics  as  well  as  of  much  else  that  follows. 

4.  What  is  a  Mass? — A  mass  is  any  quantity 
of  matter  that  is  composed  of  molecules. 

The  word  molar  is  used  to  describe  such  a  collection  of 
molecules. 

(a.)  The  term  mass  also  has  reference  to  real  quantity  as  distin- 
guished from  apparent  quantity  or  size.  A  sponge  may  be  com- 
pressed so  as  to  seem  much  smaller  than  at  first,  Imt  all  of  the 
sponge  is  still  there.  Its  density  is  changed  ;  its  quantity  or  mass 
remains  the  same.  This  double  use  of  the  word  is  unfortunate, 
but  the  meaning  in  any  given  case  may  be  easily  inferred  from  the 
connection. 

(&.)  The  quantity  of  matter  constituting  a  mass  is  not  necessarily 
great.  A  drop  of  water  may  contain  a  million  animalcules  ;  each 
animalcule  is  a  mass  as  truly  as  the  greatest  monster  of  the  land  or 
Sea.  The  dewdrop  and  the  ocean,  clusters  of  grapes  and  clusters 
Of  stars,  are  equally  masses  of  matter. 


THE  DOMAIN  OF  PHYSICS.  3 

5.  What  is   a  Molecule  I—A  molecule  is  the 
smallest  quantity  of  matter  that  can  exist  by  itself. 

Molecules  are  exceedingly  small,  far  beyond  the  reach 
of  vision  even  when  aided  by  a  powerful  microscope. 

(a.)  We  know  that  a  drop  of  water  may  be  divided  into  several 
parts,  and  each  of  these  into  several  others,  each  part  still  being 
water.  The  subdivision  may  be  carried  on  until  we  reach  a  limit 
fixed  by  the  grossness  of  our  instruments  and  vision ;  each  particle 
still  is  water.  Even  now,  imagination  may  carry  forward  the 
work  of  subdivision  until  at  last  we  reach  a  limit  beyond  which  we 
cannot  go  without  destroying  the  identity  of  the  substance.  In 
other  words,  we  have  a  quantity  of  water  so  small  that  if  we  divide 
it  again  it  will  cease  to  be  water  ;  it  will  be  something  else.  This 
smallest  quantity  of  matter  that  can  exist  by  itself  and  retain  its 
identity  is  called  a  molecule.  The  worcj  molecule  means  a  little 
mass.  (See  Avery's  Chemistry,  §  4.) 

(5.)  The  smallest  interval  that  can  be  distinctly  seen  with  the 
microscope  is  about  VV^VT  inch.  It  has  been  calculated  that  about 
2000  liquid  water  molecules  might  be  placed  in  a  row  within  such 
an  interval.  In  other  words,  an  aggregation  of  8,000,000,000  water 
molecules  is  barely  visible  to  the  best  modern  microscopes. 

6.  What    is    an    Atom  ?  —  An    atom    is    the 
smallest  quantity  of  matter    that  can    enter   into 
combinatioii. 

In  nearly  every  case  an  atom  is  a  part  of  a  molecule. 

(a.}  If  a  molecule  of  water  be  divided,  it  will  cease  to  be  water 
at  all,  but  will  yield  two  atoms  of  hydrogen  and  one  of  oxygen. 
The  molecule  of  common  salt  consists  of  one  atom  of  sodium  and 
one  of  chlorine.  Some  molecules  are  very  complex.  The  common 
sugar  molecule  contains  forty-five  atoms. 

(&.)  Atoms  make  molecules  ;  molecules  make  masses.  Of  the 
absolute  size  and  weight  of  atoms  and  molecules  little  is  known ; 
of  their  relative  size  and  weight  much  is  known,  and  forms  an  im- 
portant part  of  the  science  of  chemistry. 

7.  Forms   of  Attraction.— Each  of  these   three 
divisions  of  matter  has  its  own  form  of  attraction : 


4  THE  DOMAIN  OF  PHYSICS. 

Molar  attraction  is  called  gravitation. 

Molecular  attraction  is  called  cohesion  or  adhe- 
sion. 

Atomic  attraction  is  called  chemical  affinity  (chera- 
ism). 

8.  Forms  of  Motion. — Each  of  these  three  divi- 
sions of  matter  has  its  own  form  of  motion  : 

Molar  motion,  or  visible  mechanical  motion,  is  called 
by  different  names  according  to  the  nature  of  the 
substance  in  motion ;  e.  g.,  the  flow  of  a  river  or  the 
vibrations  of  a  pendulum. 

Molecular  motion,  called  heat,  light,  electricity,  or 
magnetism. 

Atomic  motion.     (Purely  theoretical  as  far  as  known.) 

9.  Physical    Science. — Physical   science   com- 
prises Physics  and  Chemistry. 

The  first  of  these  deals  with  masses  and  molecules;  the 
second  with  atoms  and  combinations  of  atoms. 

1C.  What  is  a  Physical  Change  ?— A  physi- 
cal change  is  one  that  does  not  change  the  identity 
of  the  molecule. 

(a.)  Inasmuch  as  the  nature  of  a  substance  depends  upon  the 
nature  of  its  molecules,  it  follows  that  a  physical  change  is  one  that 
does  not  affect  the  identity  of  a  substance.  A  piece  of  marble  may 
be  ground  to  powder,  but  each  grain  is  marble  still.  Ice  maj 
change  to  water  and  water  to  steam,  yet  the  identity  of  the  sub- 
stance is  unchanged.  A  piece  of  glass  may  be  electrified  and  a 
piece  of  iron  magnetized,  but  they  still  remain  glass  and  iron.  These 
changes  all  leave  the  composition  and  nature  of  the  molecule  un- 
changed ;  they  are  'physical  changes. 

11.  What  is  a  Chemical  Change  ?— A  chemi* 


THE  DOMAIN   OF  PHYSICS.  5 

cal  change  is  one  that  does  change  the   identity 
of  the  -molecule. 

(a.)  If  the  piece  of  marble  be  acted  upon  by  sulphuric  acid,  a 
brisk  effervescence  takes  place  caused  by  the  escape  of  carbonic  acid, 
gas  which  was  a  constituent  of  the  marble ;  calcium  sulphate 
(gypsum),  not  marble,  will  remain.  The  water  may,  by  the  action 
of  electricity,  be  decomposed  into  two  parts  of  hydrogen  and  one  of 
oxygen.  The  nature  of  the  glass  and  iron  may  easily  be  changed. 
These  change  the  nature  of  the  molecule  ;  they  are  chemical 
changes. 

12.  Definition.  —  Physics,  or  Natural  Philos- 
ophy, is  the  branch  of  science  that  treats  of  the 
laws  and  physical  properties  of  -matter,  and  of 
those  phenomena  that  depend  upon  physical 
changes. 

Recapitulation. — To  be  reproduced  and  amplified 
by  the  pupil  for  review. 

Matter.  Divisions.         Attractions.          Motions, 

r  MASSES,  GRAVITATION. 


PHYSICAL 
SCIENCE. 


PHYSICS \  <Heat. 


MOLECULES, 


j  COHESION.   |     J  Light. 
\  ADHESION.  )      j  Electricity, 
\  Magnetism, 


f  CHEMISM    . 

CHEMISTRY.    ATOMS \      OR       [  (?) 

I  AFFINITY. 


CHAFFS      PHYSICAL- 
CHANGES. 


THE  PROPERTIES  OF  MATTER. 


ECTJON  H. 


THE    PROPERTIES    OF    MATTER. 

13.  Properties  of  Matter. — Any  quality  that 
"belongs  to  matter  or  is  characteristic  of  it  is  called 
a  property  of  matter. 

Properties  of  matter  are  of  two  classes,  physical  and 
chemical. 

14.  What  are  Physical  Properties  t— Physi- 
cal   properties    are    such    as    may    be    manifested 
without  changing  the  identity  of  the  molecule  (§  10), 

(a.}  A  piece  of  coal  takes  up  room,  it  is  hard  and  heavy,  it  can- 
not move  itself.  These  several  qualities  or  properties  the  coal  may 
exhibit  and  still  remain  coal,  or  still  retain  its  identity.  They  are, 
therefore,  physical  properties  of  coal. 

15.  What  are  Chemical  Properties  ?— Chem- 
ical Properties  are  such  as  cannot   be  manifested 
without  changing  the  identity  of  the  molecule  (§11). 

(a.)  A  piece  of  coal  may  be  burned  ;  therefore  combustibility  is 
a  property  of  the  coal.  This  property  has  been  held  by  the  coal 
for  countless  ages,  but  it  never  has  been  shown.  Further,  this 
piece  of  coal  never  can  show  this  property  of  combustibility  with- 
•out  ceasing  to  exist  as  coal,  without  losing  its  identity.  When  the 
coal  is  burned,  the  molecules  are  changed  from  coal  or  carbon  to 
carbonic  acid  gas  (C03). 

16.  Experiment. — Take  a  piece  of   ordinary  sul- 
phur (brimstone)  and  attempt  to  pull  it  in  pieces;    the 
degree  of  its   resistance  to   this  effort,  or  its   tenacity, 
measures  the  attraction  of  the  molecules  for  each  other. 
Strike  it  with  a  hammer,  and  it  breaks  into  many  pieces, 
thus  manifesting  its  Irittknm ;  but  each  piece  is  ordinary 


THE  PROPERTIES  OF  MATTER.  7 

sulphur.  Heat  it  in  a  spoon,  and  it  assumes  the  liquid 
form,  but  it  is  sulphur  yet.  In  none  of  these  changes  has 
the  nature  of  the  molecule,  or  the  identity  of  the  sub- 
stance, undergone  any  change.  On  the  other  hand,  if 
the  sulphur  be  heated  sufficiently  it  will  take  fire  and 
burn,  producing  the  irritating,  suffocating  gas  familiar  to 
all  through  the  use  of  common  matches.  We  thus  see 
that  the  sulphur  is  combustible.  This  combustibility  is 
a  chemical  property,  in  the  manifestation  of  which  the 
identity  of  the  substance  is  destroyed.  Before  the  mani- 
festation we  had  sulphur;  after  it  we  have  sulphurous 
anhydride  (S02).  The  original  molecules  were  elemen- 
tary, composed  of  like  atoms  ;  the  resultant  molecules 
are  compound,  composed  of  unlike  atoms,  sulphur  and 
oxygen. 

17.  Division  of  Physical  Properties. — Physi- 
cal properties  of  matter  are,  in  turn,  divided  into  two 
classes,  universal  and  characteristic. 

18.  What  are  Universal  Properties  ?—  Uni- 
versal properties  of  matter  are  such   as  belong  to 
all  matter. 

All  substances  possess  them  in  common ;  no  body  'can 
exist  without  them.  We  cannot  even  imagine  a  body 
that  does  not  require  space  for  its  existence.  This  qual- 
ity of  matter,  which  will  so&i  be  named,  is,  therefore, 
universal. 

19.  What  are  Characteristic  Properties? — 

Characteristic  properties  of  matter  are  such  as 
belong  to  matter  of  certain  kinds  only. 

They  enable  us  to  distinguish  one  substance  from  an- 


8  THE  PROPERTIES   OF  MATTER. 

other.  Glass  is  brittle,  and  by  this  single  property  may 
be  distinguished  from  india-rubber. 

20.  List  of  Universal  Properties.— The  prin- 
cipal universal  properties  of  matter  are  extension,  im- 
penetrability,    weight,      indestructibility,      inertia, 
mobility,    divisibility,  porosity,  compressibility,  ex- 
pansibility, and  elasticity. 

21.  List  of  Characteristic  Properties.— The 

characteristic  properties  of  matter  (often  called  specific  or 
accessory  properties)  are  numerous.  They  depend,  for  the 
most  part,  upon  cohesion  and  adhesion.  The  most  im- 
portant characteristic  properties  are  hardness,  tenacity, 
brittleness,  malleability,  ductility. 

22.  What  is    Extension? — Extension  is  that 
property  of  matter  by  virtue  of  which   it  occupies 
space. 

It  has  reference  to  the  qualities  of  length,  breadth,  and 
thickness.  It  is  an  essential  property  of  matter,  involved 
in  the  very  definition  of  matter. 

(a.)  All  matter  must  have  these  three  dimensions.  We  say  that 
a  line  has  length,  a  surface  has  length  and  breadth  ;  but  lines  and 
surfaces  are  mere  conceptions  of  the  mind,  and  can  have  no  material 
existence.  The  third  dimension,  which  affords  the  idea  of  solidity 
or  volume,  is  necessary  to  every  form  of  every  kind  of  matter.  No 
one  can  imagine  a  body  that  h^.s  not  these  three  dimensions,  that 
does  not  occupy  space,  or  "  take  up  room."  Figure  or  shape  neces- 
sarily follows  from  extension. 

23.  English  Measures. — For  the  purpose  of  com- 
paring volumes,  as  well  as  surfaces  and  lengths,  measures 
are  necessary.    In  the  United  States  and  England  the 
yard  has  been  adopted  as  the  unit,  and  its  divisions,  as 


THE  PROPERTIES   OF  MATTER. 


9 


feet  and  inches,  together  with  its  multiples,  as  rods  and 
miles,  are  in  familiar  use.  This  unit  is  determined  by 
certain  bars,  carefully  preserved  by  the  governments  of 
these  two  nations. 

24.  Metric  Measures.— The  international  system 
has  the  merits  of  a  less  arbitrary  foundation  and  of  far 
greater  convenience.     From  its  unit  it  is  known  as  the 
metric  system.     This  system  is  in  familiar  use  in  most  of 
the  countries  of    continental  Europe  and  by  scientific 
writers  of  all  nations,  and  bids  fair  to  come  into  genera] 
use  in  this  country.    For  these  reasons,  as  well  as  for  its 
greater  convenience,  an  acquaintance  with  this  system  is 
now  desirable,  and  will  soon  be  necessary.     It  has  been 
already  legalized  by  act  of  Congress. 

25.  Definition  of  Meter. — The  meter  is  defined 
as  the  forty-millionth  of  the  earth's  meridian  which 
passes  through  Paris,  or  as  the  ten-millionth  of  a  quadrant 
of  such  a  meridian.     It  is  equal  to  39.37  inches.     Like 
the  Arabic  system  of  notation   and  the  table  of  U.  S. 
Money,  its  divisions    and    multiples   vary  in  a   tenfold 
ratio. 

26.  Metric    Measures    of   Length.  —  Ratio 


f  Millimeter  (mm.)  =  .001  m.=    0.03937  inches. 

DIVISIONS.    J  Centimeter  (cm.)    =  .01  m.=    0.3937       " 

[  Decimeter  (dm.)  =  .1  m.=     3.937 

UNIT.               Meter  (m.)    =  1.  m.=  39.37 

IDekameter  (Dm.}—  10.  w.=393.7             " 

Hektometer  (Hm.)—  100.  m.=328  ft.  1  inch. 

Kilometer  (Km.)=  1000.  m.=    0.62137  miles. 

Myriameter  (Mm.)= 10000.  m.=    6.2137 


10  THE  PROPERTIES   OF  HATTER. 

Note. — The  table  may  be  read  :    10  millimeters  make  1 
centimeter  ;   10  centimeters  make  1  decimeter,  etc.     The 
denominations  most  used  in  practice  are  printed  in  italics. 
The  system  of  nomenclature  is  very  simple.     The  Latin 
prefixes,  milli-,  centi-,  and  deci-,  signifying  respectively 
Timr>  T£U»  an(i  iV>  an(i  already  familiar  in  the  mill,  cent, 
S   and  dime  of   U.   S.  Money,  are  used   for  the  divisions, 
*!   while  the  Greek  prefixes  deka-,  JieJcto-,  kilo-,  and  myrla-, 
'J.  signifying  respectively  10,  100,  1000,  and  10000,  are  used 
£  for  the  multiples  of  the  unit.     Each  name  is  accented  on 
ij  the  first  syllable. 

|      21.  Metric    Measured   of    Surface. — 

•§  Ratio  =  1C2  =  1OO. 

ii 

f  Square  millimeter  (sq.  mm.)= 0.000001  sq.  m. 
.|   DIVISIONS.^  Square  centimeter  (sq.cm.)  =0.0001          " 

g  [  Square  decimeter    (sq.  dm.)  =0.01  " 

o 

n    UNIT.  Square  meter  (sq.  m.)    =1. 

etc.,  etc. 

J       Note. — The  table  may  be  read:  100  sq.  mm.  =  1  sq.  cm.; 
'§   100  sq.  cm.  =  1  sq.  dm.,  etc.     The  reason  for  the  change 
8   of  ratio  from  10  to  100  may  be  clearly  shown  by  represent- 
ing 1  sq.  dm.,  and  dividing  it  into  sq.  cm.  by  lines,  which 
shall  divide  each  side  of  the  sq.  dm.  into  10  equal  parts  or 
centimeters. 

28.   Metric    Measures  of  Volume.— 
FlG  j    Ratio  =  1O3  =  1OOO. 

f  Cubic  millimeter  (cu.  mm.)  =  0.000000001  cu.  m. 
DIVISIONS.  <  Cubic  centimeter    (cu.  cm.)  =  0.000001  " 

[  Cubic  decimeter    (cu.  dm.)  =  0.001  " 

UNIT.  Cubic  meter  (cu.  m.)     =1.308  cu.  yds. 

etc.,  etc. 

29.  Metric  Measures  of  Capacity.— Ratio  = 

1C. — For  many  purposes,  such  as  the  measurement  of 
articles  usually  sold  by  dry  and  liquid  measures,  a  smaller 
unit  than  the  cubic  meter  is  desirable.  For  such  purposes 


THE  PROPERTIES  OF  MATTER.  11 

the  cubic  decimeter  has  been  selected  as  the  standard, 
and  when  thus  used  is  called  a  liter  (pronounced  leeter). 

f  Milliliter    (ml)  =      1  cu.  cm.=  0.061022  cu.  in. 
DIVISIONS.     \  Centiliter    (d.)    =     10     "       =  0.338  fid.  oz. 
[  Deciliter     (dl.)   =  100     "       =  0.845  gill. 

UNIT.  Liter          (1.)     =1000     "       =  1.0567  liquid  qts. 

f  Dekaliter    (Dl)  =     10  cu.  dm.=  9.08  dry  qts. 
MULTIPLES.  -I  Hektoliter  (HI)  =  100cu.dm.=  2  bu.  3.35  pks. 
[  Kiloliter    (El.)  =      1  cu.  ra.  =  264.17  gals. 

30.  Comparative  Helps. — It  may  be  noticed  that 
the  m.  corresponds  somewhat  closely  to  the  yard,  which  ifc 
ivill  replace.     Kilometers  will  be  used  instead  of  miles. 
The  cu.  cm.  may  be  represented  by  the  ordinary  die  used 
in  playing  backgammon.    The  /.  does  not  differ  very  much 
from  the  quart,  or  the  DL  from  the  peck,  which  they  will 
respectively  replace.     In  fact,  the  I.  is,  in  capacity,  inter- 
mediate between  the  dry  and  liquid  quarts. 

31.  What    is    Impenetrability? — Impenetra- 
bility is  that  property  of  matter  by  virtue  of  which 
two  bodies  cannot  occupy  the   same  space   at  the 
same  time. 

(a,.)  Illustrations  of  this  property  are  very  simple  and  abundant. 
Thrust  a  finger  into  a  tumbler  of  water  ;  it  is  evident  that  the  water 
and  the  finger  are  not  in  the  same  place  at  the  same  time.  Drive  a 
nail  into  a  piece  of  wood  ;  the  particles  of  wood  are  either  crowded 
more  closely  together  to  give  room  for  tlie  nail,  or  some  of  them  are 
driven  out  before  it.  Clearly,  the  iron  and  the  wood  are  not  in  the 
same  place  at  tlie  same  time. 

32.  Experiment. —  Through  one  cork  of  a  two- 
necked  bottle  pass  a  small  funnel  or  "  thistle-tube,"  and 
let  it  extend  nearly  to  the  bottom  of  the  bottle.     Through 


OP 
TT>T  TT7  IT  TD  o,  Tn-^ 


THE  PROPERTIES   OF  MATTER. 


the  other  cork  lead  a  tube  to  the  water-pan,  and  let  it 

terminate  beneath  or 
within  the  neck  of 
a  clear  glass  bottle 
filled  with  water, 
and  inverted  in  the 
water-pan.  See  that 
the  corks  are  air- 
tight; if  necessary, 
seal  them  with  wax 
or  plaster  of  Paris. 
If  a  two-necked  bot- 
FlG-  2.  tie  be  not  convenient, 

substitute  therefor  a 

wide-mouthed  bottle  having  two  holes  through  the  cork. 
The  delivery  tube  is  best  made  of  glass.  It  may  be  easily 
bent  by  first  heating  it  red-hot  in  an  alcohol  or  gas  flame. 
Pour  water  steadily  through  the  funnel ;  as  it  descends, 
air  is  forced  out  through  the  delivery  tube,  and  may  be 
seen  bubbling  through  the  water  in  the  inverted  bottle. 
At  the  end  of  the  experiment,  the  volume  of  water  in  the 
two-necked  bottle  will  be  nearly  equal  to  the  volume  of  air 
in  the  inverted  bottle.  This  clearly  shows  the  impene- 
trability of  air. 

33.  What  is  Weight  ?—  Weight  is  (as  the  term 
is  generally  used)  the  measure  of  gravity  or  molar  at- 
traction (§  7)  of  which  it  is  a  necessary  consequence. 

(a.}  As  all  masses  of  matter  exert  this  force,  weight  necessarily 
pertains  to  all  matter ;  but,  in  general  use,  the  term  weight  has 
reference  to  bodies  upon  the  earth.  If  a  body  be  placed  near  the 
earth's  surface  and  left  unsupported,  the  mass-attraction  of  the 
earth  for  each  molecule  in  the  body  will  draw  the  two  together,  and 


THE  PROPERTIES   OF  MATTER.  13 

the  body  is  said  to  fall  to  the  earth.  But  in  this  case  we  have  no 
means  of  measuring  the  force  that  draws  the  two  bodies  together. 
If  now  the  body  be  supported,  the  force  acts  as  before  and  produces 
pressure  upon  the  supporting  substance.  This  pressure  measures 
the  attractive  force  acting  between  the  earth  and  the  body,  and  is 
called  weight.  If  a  second  body  like  the  first  be  placed  beside  it, 
the  mass  attraction  of  the  earth  is  exerted  upon  twice  as  many 
molecules,  and,  reciprocally,  the  attraction  of  twice  as  many  mole- 
cules is  exerted  upon  the  earth;  i.  e.,  the  attraction  has  become  twice 
as  great,  and  the  measure  of  that  attraction,  or  the  weight,  has  been 
doubled. 

(b.)  If  the  same  body  were  upon  the  moon,  its  weight  would  be 
the  measure  of  the  attraction  existing  between  the  body  and  the 
moon.  But  as  the  mass  of  the  moon  is  less  than  that  of  the  earth, 
the  attraction  between  the  body  and  the  moon  would  be  less  than 
that  between  that  body  and  the  earth,  and  the  weight  would  be 
proportionally  diminished. 

34.  English  Measures  of  Weight.— For  the 

comparison  of  weights,  as  well  as  of  extension,  standards 
are  necessary.  In  England  and  the  United  States  the 
pound  is  taken  as  the  unit.  Unfortunately,  we  have 
pounds  Troy,  Avoirdupois,  and  Apothecaries',  the  use  vary- 
ing with  the  nature  of  the  transaction.  As  with  the  yard, 
these  units  are  arbitrary,  determined  by  certain  carefully 
preserved  standards. 

35.  Metric    Measures   of   Weight.  —  Ratio 
=  10. 

f  Milligram  (mg.)  =    0.0154  grains  avoirdupois. 

DIVISIONS.     J  Centigram  (eg.)  =    0.1543      "  " 

[Decigram  (dg.)  =     1.5432      " 

UNITS.  Gram  (g)  =  15.432 

Dekagram  (Dg.)  =    0.3527  oz.  '« 

Hektogram  (Hg.)  =  •   3.5274    "  " 

Kilogram  (Kg.)  =    2.2046  Ibs. 

Myriagram  (Mg)  =  22.046      "  " 


14  THE  PROPERTIES   OF  MATTER. 

36.  What  is  a  Gram  ?— A  gram  is  the  weight 
of  one  cu.  cm.  of  pure  water,  at  its  temperature  of 
greatest  density  (4°  C,  or  39.2°  F.).    A  5-cent  nickel  coin 
weighs  5  g. 

EXERCISES. 

1.  How  much  water,  by  weight,  will  a  liter  flask  contain? 

2.  If  sulphuric  acid  is  1.8  times  as  heavy  as  water,  what  weight 
of  the  acid  will  a  liter  flask  contain  ? 

3.  If  alcohol  is  0.8  times  as  heavy  as  water,  how  much  will  1250 
cu.  cm.  of  alcohol  weigh  ? 

4.  What  part  of  a  liter  of  water  is  250  g.  of  water  ? 

5.  What  is  the  weight  of  a  cu.  dm.  of  water  ? 

6.  What  is  the  weight  of  a  dl.  of  water  ? 

37.  What  is  Indestructibility? — Indestructi- 
bility is  that  property  of  matter  by  virtue  of  which 
it  cannot  be  destroyed. 

(a.)  Science  teaches  that  the  universe,  when  first  hurled  into  space 
from  the  hand  of  the  Creator,  contained  the  same  amount  of  matter, 
and  even  the  same  quantity  of  each  element,  that  it  contains  to-day. 
This  matter  has  doubtless  existed  in  different  forms,  but  during  all 
the  ages  since,  not  one  atom  has  been  gained  or  lost.  Take  carbon 
for  instance.  From  geology  we  learn  that  in  the  carboniferous  age, 
long  before  the  advent  of  man  upon  the  earth,  the  atmosphere  was 
highly  charged  with  carbonic  acid  gas,  which,  being  absorbed  by 
plants,  produced  a  vegetation  rank  and  luxuriant  beyond  comparison 
with  any  now  known.  The  carbon  thus  changed  from  the  gaseous 
to  the  solid  form  was,  in  time,  buried  deep  in  the  earth,  where  it 
has  lain  for  untold  centuries,  not  an  atom  lost.  It  is  now  mined  as 
coal,  burned  as  fuel,  and  thus  transformed  again  to  its  original 
gaseous  form.  No  human  being  can  create  or  destroy  a  single  atom 
of  carbon  or  of  any  other  element.  Matter  is  indestructible. 
Water  evaporates  and  disappears  only  to  be  gathered  in  clouds  and 
condense  and  fall  as  rain.  Wood  burns,  but  the  ashes  and  smoke 
contain  the  identical  atoms  of  which  the  wood  was  composed.  In  a 
different  form,  the  matter  still  exists  and  weighs  as  much  as  before 
the  combustion. 

38.  What    is    Inertia? — Inertia  is  that  prop- 
erty of  matter  by  virtue  of  which  it  is  incapable 


THE  PROPERTIES   OF  MATTER.  15 

of  changing  its  condition  of  rest  or  motion,  or  the 
property  by  virtue  of  which  it  has  a  tendency  when  at 
rest  to  remain  at  rest,  or  when  in  motion  to  continue  in 
motion. 

(a.)  If  a  ball  be  thrown,  it  requires  external  force  to  put  it  in  mo- 
tion; the  ball  cannot  put  itself  in  motion.  When  the  ball  is  passing 
through  the  air  it  has  no  power  to  stop,  and  it  will  not  stop  until 
some  external  force  compels  it  to  do  so.  This  external  force  may 
be  the  bat,  the  catcher,  the  resistance  of  the  air,  or  the  force  of 
gravity.  It  must  be  something  outside  the  ball  or  the  ball  will  move 
on  forever.  Illustrations  of  the  inertia  of  matter  are  so  numerous 
that  there  should  be  no  difficulty  in  getting  a  clear  idea  of  this 
property.  The  "  running  jump "  and  "dodging"  of  the  play- 
ground, the  frequent  falls  which  result  from  jumping  from  cars  in 
motion,  the  backward  motion  of  the  passengers  when  a  car  is  sud- 
denly started  and  their  forward  motion  when  the  car  is  suddenly 
stopped,  the  difficulty  in  starting  a  wagon  and  the  comparative  ease 
of  keeping  it  in  motion,  the  "  balloon"  and  "  banner"  feats  of  the 
circus-rider,  etc.,  etc.,  may  be  used  to  illustrate  this  property  of 
matter. 

39.  Experiment.^— Upon  the 

tip  of  the  fore-finger  of  the  left 
hand,  place  a  common  calling-card. 
Upon  this  card,  and  directly  over 
the  finger,  place  a  cent.  With  the 
nail  of  the  middle  finger  of  the 
right  hand  let  a  sudden  blow  or  "  snap  "  be  given  to  the 
card.  A  few  trials  will  enable  you  to  perform  the  experi- 
ment so  as  to  drive  the  card  away,  and  leave  the  coin 
resting  upon  the  finger.  Repeat  the  experiment  with  the 
variation  of  a  bullet  for  the  cent,  and  the  open  top  of  a 
bottle  for  the  finger-tip. 

40.  What  is  Mobility  ?— Mobility  is  that  prop- 
erty of  matter  by  virtue  of  which  the  position  of 
bodies  may  be  changed. 


16  THE  PROPERTIES   OF  MATTER. 

(a.)  A  body  is  any  separate  portion  of  matter,  be  it  large  or  small, 
as  a  book,  a  table,  or  a  star.  The  term  is  nearly  synonymous  with 
mass,  but  has  not  so  distinct  a  reference  to  the  absolute  quantity  of 
matter.  Bodies  or  masses  are  composed  of  molecules  ;  molecules 
are  composed  of  atoms. 

(&.)  On  account  of  inertia,  the  body  cannot  change  its  own  posi- 
tion ;  on  account  of  mobility  any  mass  of  matter  may  be  moved  if 
sufficient  force  be  applied.  This  changing  of  position  is  called 
motion  ;  motion  presupposes  force.  (See  §  64.) 

41.  What  is  Divisibility  I— Divisibility  is  that 
property  of  matter  by  virtue  of  which  a  body  may 
be  separated  into  parts.  ifil. 

(a.)  Theoretically,  the  atom  is  the  limit  of  divisibility  of  matter. 
Practically  the  divisibility  of  matter  is  limited  before  the  molecule 
is  reached  ;  our  best  instruments  are  not  sufficiently  delicate,  our 
best  trained  senses  are  not  acute  enough  for  the  isolation  or  percep- 
tion of  a  molecule.  Nevertheless,  this  divisibility  may  be  carried 
to  such  an  extent,  by  natural,  mechanical  (physical)  or  chemical 
means,  as  to  excite  our  wonder  and  test  the  powers  of  imagination 
itself.  It  is  said  that  the  spider's  web  is  made  of  threads  so  fine 
that  enough  of  this  thread  to  go  around  the  earth  would  weigh  but 
half  a  pound,  and  that  each  thread  is  composed  of  six  thousand  fila- 
ments. A  single  inch  of  this  thread  with  all  its  filaments  may  be 
cut  into  thousands  of  distinct  pieces,  and  each  piece  of  each  fila- 
ment be  yet  a  mass  of  matter  composed  of  molecules  and  atoms. 
The  microscope  reveals  to  us  the  existence  of  living  creatures  so 
small  that  it  would  require  thousands  of  millions  of  them  to  aggre- 
gate the  size  of  a  hemp-seed.  Yet  each  animalcule  has  organs  of 
absorption,  etc. ;  in  some  of  these  organs  fluids  circulate  or  exist. 
How  small  must  be  the  molecules  of  which  these  fluid  masses  are 
composed  !  What  about  the  size  of  the  atoms  which  constitute  the 
molecules  ?  A  coin  in  current  use  loses,  in  the  course  of  a  score  of 
years,  a  perceptible  quantity  of  metal  by  abrasion.  What  finite 
mind  can  form  a  clear  idea  of  the  amount  of  metal  rubbed  off  at 
each  transfer  ? 

4:2.  What  is  Porosity? — Porosity  is  that  prop- 
erty of  matter  by  virtue  of  which  spaces  exist 
between  the  molecules. 


'DIVERSITY 
THE  PROPERTIES 

(a.)  When  iron  is  heated,  the  molecules  are  pushed  further  apart, 
the  pores  are  enlarged,  and  we  say  that  the  iron  has  expanded.  If 
a  piece  of  iron  or  lead  be  hammered,  it  will  be  made  smaller,  because 
the  molecules  are  forced  nearer  together,  thus  reducing  the  size  of 
the  pores.  Cavities  or  cells,  like  those  of  bread  or  sponge,  are  some- 
times spoken  of  as  "sensible  pores,"  but  these  are  not  properly  in- 
cluded under  this  head. 

43.  What  is  Compressibility?— Compressibil- 
ity is  that  property  of  matter  by  virtue  of  which 
a  body  may  be  reduced  in  size. 

44.  What  is  Expansibility?— Expansibility  is 
that  property  of  matter  by  virtue  of  which  a  body 
may  be  increased  in  size. 

(a.)  Compressibility  and  expansibility  are  the  opposites  of  each 
other,  resulting  alike  from  porosity.  Illustrations  have  been  given 
under  the  head  of  porosity.  Let  each  pupil  prove  by  experiment 
that  air  is  compressible  and  expansible. 

45.  What    is   Elasticity  ?— Elasticity   is   that 
property  of  matter  by  virtue  of  which  bodies  resume 
their    original  form    or   size   when    that  form   or 
size  has  been  changed  by  any  external  force. 

(a.)  All  bodies  possess  this  property  in  some  degree,  because  all 
bodies,  solid,  liquid  or  aeriform,  when  subjected  to  pressure  (within 
limits  varying  with  the  substance),  will  resume  their  original  size 
upon  the  removal  of  the  pressure.  The  amount  of  compression  mat- 
ters not  except  in  the  case  of  solids.  It  was  formerly  thought  that 
liquids  were  incompressible  ;  hence  aeriform  bodies  were  called 
elastic  fluids,  while  liquids  were  called  non-elastic  fluids.  But  the 
compressibility  and  perfect  elasticity  of  liquids  having  been  shown, 
the  term  "non-elastic  fluid"  involves  a  contradiction  of  terms  and 
would  better  be  dropped.  Fluids  have  no  elasticity  of  form  ;  on 
the  other  hand,  all  fluids  have  perfect  elasticity  of  size.  What 
properties  of  matter  are  illustrated  by  the  action  of  the  common 
pop-gun  ? 

46.  What  are  Cohesion  and  Adhesion?— 

Cohesion  is  the  force  that  holds  together  like  mole- 


18  THE  PROPERTIES  OF  MATTER. 

cules ;    adhesion   is  the  force  that    holds    together 
unlike  molecules. 

(a.)  Cohesion  is  the  force  that  holds  most  substances 
together  and  gives  them  form.     Were  cohesion  suddenly 
to  cease,  brick  and  stone  and  iron  would  crumble  to  finest 
_.,  powder,  and  all  our  homes  and  cities  and  selves  fall  to 

hopeless  ruin.  In  aeriform  bodies,  cohesion  is  not  ap- 
parent, being  overcome  by  molecular  repulsion  (heat).  In 
large  masses  of  liquids  the  cohesive  force  is  overcome  by  gravity, 
which  tends  to  bring  all  the  molecules  as  low  as  possible  and  thus 
renders  their  surfaces  level.  But  in  small  masses  of  liquids,  the 
cohesive  force  predominates  and  draws  all  the  molecules  as  near 
each  other  as  possible,  and  thus  gives  to  each  mass  the  spheroidal 
form,  as  in  the  case  of  the  dew  or  rain-drop.  Globules  of  mercury 
upon  the  hand  or  table,  and  drops  of  water  upon  a  heated  stove,  are 
familiar  illustrations  of  this  effect  of  cohesion  upon  small  liquid 
masses.  But  in  the  solid  state  of  matter,  cohesion  shows  most 
clearly.  Cohesion  acts  only  at  ijr  sensible  (molecular)  distances.  Let 
the  parts  of  a  body  be  separated  by  a  sensible  distance,  and  cohesion 
ceases  to  act ;  we  say  that  the  body  is  broken.  If  the  molecules  of 
the  parts  can  again  be  brought  within  molecular  distance  of  each 
other,  cohesion  will  again  act  and  hold  them  there.  This  may  be 
done  by  simple  pressure,  as  in  the  case  of  wax  or  freshly-cut  lead ; 
it  may  be  done  by  welding  or  melting,  as  in  the  case  of  iron.  Cir- 
cular plates  of  glass  or  metal,  about  three  inches  in  diameter,  often 
have  their  faces  so  accurately  fitted  to  each  other  that,  when  pressed 
together,  a  considerable  force  is  needed  to  separate  them.  (See 
Fig.  4.) 

(&.)  Adhesion  is  the  force  that  causes  the  pencil  or  crayon  to  leave 
traces  upon  the  paper  or  blackboard,  and  gives  efficacy  to  paste, 
glue,  mortar  and  cements  generally.  In  a  brick  wall,  cohesion  binds 
together  the  molecules  of  the  mortar  layer  into  a  single,  hardening 
mass,  while  on  either  hand  adhesion  reaches  out  and  grasps  the  ad- 
joining bricks  and  holds  them  fast— a  solid  wall.  Like  cohesion,  it 
acts  only  through  distances  too  small  to  be  measured  ;  unlike  cohe- 
sion, it  acts  between  unlike  molecules. 

47.  What  is  Hardness  ?—  Hardness  is  that 
property  of  matter  by  virtue  of  which  some  bodies 
resist  any  attempt  to  force  a  passage  between  their 
particles. 


THE  PROPERTIES   OF  MATTER.  19 

It  is  measured  by  the  degree  of  difficulty  with  which  it 
is  scratched  by  another  substance.  Fluids  are  not  said  to 
have  hardness. 

(a.)  Hardness  does  not  imply  density.  The  diamond  is  much 
harder  than  gold,  but  gold  is  four  times  as  dense  as  diamond. 

48.  What  is  Tenacity  ? — Tenacity  is  that  prop- 
erty of  7natter  by  virtue  of  which  some  bodies  re- 
sist a  force  tending  to  pull  their  particles  asunder. 

(a.)  Like  hardness  and  the  other  characteristic  properties  of 
matter,  it  is  a  variety  of  cohesion  which  is  the  general  term  for  the 
force  which  holds  the  molecules  together  and  prevents  disintegration. 
The  tenacity  of  a  substance  is  generally  ascertained  by  shaping  it  in 
the  form  of  a  rod  or  wire,  the  area  of  whose  cross-section  may  be 
accurately  measured.  Held  by  one  end  in  a  vertical  position,  the 
greatest  weight  which  the  rod  will  support  is  the  measure  of  its 
tenacity.  For  any  given  material,  it  has  been  found  that  the  tenacity 
is  proportioned  to  the  area  of  the  cross-section  ;  e.  g.,  a  rod  with  a  sec- 
tional area  of  a  square  inch  will  carry  twice  as  great  a  load  as  a 
rod  of  the  same  material  with  a  sectional  area  of  a  half  square  inch; 
a  rod  one  decimeter  in  diameter  will  carry  four  times  as  great  a  load  as 
a  similar  rod  five  centimeters  in  diameter.  The  explanation  of  this  is 
simple  ;  imagine  these  rods  to  be  cut  across,  and  it  will  be  evident 
that,  on  each  side  of  the  cut,  the  first  rod  will  expose  the  surfaces 
of  twice  as  many  molecules  as  will  the  second,  and  that  the  third 
will  expose  four  times  as  many  molecular  surfaces  as  the  fourth. 
But  for  the  same  material,  each  molecule  has  the  same  attractive 
force.  Doubling  the  number  of  these  attractive  molecules,  which 
is  done  by  doubling  the  sectional  area,  doubles  the  total  attractive 
or  cohesive  force,  which,  in  this  case,  is  called  tenacity ;  quadru- 
pling the  sectional  area  quadruples  the  tenacity.  Hence  the  law  : 
Tenacity  is  proportioned  to  the  sectional  area. 

49.  What  is  Brittleness  t— Brittleness  is  that 
property  of  matter  by  virtue  of  which  some  bodies 
may  be  easily  broken,  as  by  a  blow. 

(a.)  Glass  furnishes  a  familiar  example  of  this  property.  The 
idea  that  brittleness  is  the  opposite  of  hardness,  elasticity  or  tenac- 
ity, should  be  guarded  against,  Glass  is  harder  than  wood,  but 


THE  PROPERTIES   OF  MATTER. 


very  brittle  ;   it  is  very  elastic,  but  very  brittle  also.    Steel  is  far 
more  tenacious  than  lead,  and  far  more  brittle. 

50.  What    is    Malleability  t— Malleability  is 
that  property  of  matter  ~by  virtue  of  ivhich  some 
bodies  may  be  rolled  or  hammered  into  sheets. 

(a.}  Steel  lias  been  rolled  into  sheets  thinner  than  the  paper  upon 
which  these  words  are  printed.  Gold  is  the  most  malleable  metal, 
and,  in  the  form  of  gold  leaf,  has  been  beaten  so  thin  that  282,000 
sheets,  placed  one  upon  the  other,  would  measure  but  a  single  inch 
in  height. 

51.  What    is    Ductility  ?—  Ductility   is   that 
property  of  matter  by  virtue  of  which  some  bodies 
may  be  drawn  into  wire. 

(a.)  Platinum  wire  has  been  made  ^m  °f  an  mc^  *n  diameter. 
Glass,  when  heated  to  redness,  is  very  ductile. 

52.  Experiment. — Heat  the  middle  of  a  piece  of 
glass  tubing,  about  six  inches  long,  in  an  alcohol  flame, 
until  red-hot    Roll  the  ends  of  the  glass  slowly  between 
the  fingers,  and  when  the  heated  part  is  soft,  quickly  draw 
the  ends  asunder.    That  the  fine  glass  wire  thus  produced 
is  still  a  tube,  may  be  shown  by  blowing  through  it  into  a 
glass  of  water,  and  noticing  the  bubbles  that  will  rise  to 
the  surface. 

Recapitulation. — To  be  reproduced  and  amplified 
by  the  pupil  from  memory. 


PROPERTIES 
OF  MATTER. 


CHEMICAL. 


PHYSICAL. 


GENERAL... 


CHARACTER- fADHESION' 
ISTIC.         1  COHESION. 


Extension,  Impenetrabil- 
ity, Weight,  Indestruc- 
tibility, Inertia,  Mobil- 
ity, Divisibility,  Po- 
rosity, Compressibility, 
Expansibility,  Elas- 
ticity. 

Hardness. 

Tenacity. 

Brittleness. 

Malleability. 

Ductility. 


THE    THREE    CONDITIONS    OF   MATTER.  21 


ECTION  III. 


THE  THREE    CONDITIONS   OF  MATTER. 

53.  Conditions   of  Matter. — Matter  exists  in 
three  conditions  or  forms— the  solid,  the  liquid, 
and  the  aeriform. 

54.  What  is  a  Solid  ? — A  solid  is  a  bodij  whose 
molecules  change  their    relative   positions    with 
difficulty. 

Such  bodies  have  a  strong  tendency  to  retain  any  form 
that  may  be  given  to  them.  A  movement  of  one  part  of 
such  a  body  produces  motion  in  all  of  its  parts. 

55.  What  is   a  Liquid?—^  liquid  is  a  body 
whose  molecules,  easily  change  their  relative  po- 
sitions, yet  tend  to  cling  together. 

Such  bodies  adapt  themselves  to  the  form  of  the  vessel 
containing  them,  but  do  not  retain  that  form  when  the 
restraining  force  is  removed.  They  always  so  adapt  them- 
selves as  to  have  their  free  surfaces  horizontal.  Water 
is  the  best  type  of  liquids. 

56.  Experiment.— Sus- 
pend a  glass  or  metal  plate, 
of    about  four    inches    area, 
from  one  end  of  a  scale-beam, 
and    accurately    balance    the 
same  with  weights  in  the  oppo- 
site scale-pan.     The  support- 
ing cords  may  be  fastened  to 

the  plate  with  wax.    Beneath  FIG.  5. 


22  TEE  THREE  CONDITIONS   Of  MATTER. 

the  plate  place  a  saucer  so  that  when  the  saucer  is  filled 
with  water  the  plate  may  rest  upon  the  liquid  surface,  the 
scale-beam  remaining  horizontal.  Carefully  add  small 
weights  to  those  in  the  scale-pan.  Notice  that  the  water 
beneath  the  plate  is  raised  above  its  level.  Add  more 
weights  until  the  plate  is  lifted  from  the  water.  Notice 
that  the  under  surface  of  the  plate  is  wet.  These  mole- 
cules on  the  plate  have  been  torn  from  their  companions 
in  the  saucer.  The  weights  added  to  the  original  coun- 
terpoise were  needed  to  overcome  the  tendency  of  the 
water  molecules  to  cling  together. 

Note  to  the  Pupil. — After  seeing  a  physical  experiment,  always  ask 
yourself,  "  What  was  the  object  of  that  experiment?  What  does  it 
teach?"  Never  allow  yourself  to  look  upon  an  experiment  as  being 
simply  entertaining ;  thus  reducing  the  experimenter,  so  far  as  you 
are  concerned,  to  the  level  of  a  showman. 

57.  What  is  an  Aeriform   Body?— An  aeri- 
form body  is  one  whose  molecules  easily  change 
their  relative  positions,  and  tend  to  separate  from 
each  other  almost  indefinitely. 

Atmospheric  air  is  the  best  type  of  aeriform  bodies. 

58.  Gases    and   Vapors.— Aeriform  (having  the 
form  of  air)  bodies  are  of  two  kinds,  gases  and  vapors. 
Gases  remain  aeriform  under  ordinary  conditions,  although 
some,  if  not  all,  may  be  liquefied  by  intense  cold  and  pres- 
sure.    Vapors  are  aeriform  bodies  produced  by  heat  from 
substances  that  are  generally  solid  or  liquid,  as  iodine  or 
water.     They  resume  the  solid  or  liquid  form  at  the  ordi- 
nary temperature. 

59.  Changes  of  Condition.— The  same  substance 
may  exist  in  two  or  even  three  of  these  forms.     Most 


THE   THREE   CONDITIONS   OF  MATTER.  23 

solids,  as  lead  and  iron,  may  be  changed  by  heat  to  liquids ; 
others,  as  iodine,  may  be  apparently  changed  directly  to 
vapors ;  still  others,  as  ice,  may  be  easily  changed  first  to 
the  liquid,  and  then  to  the  vapor  form.  It  is  probable  that 
any  solid  might  be  liquefied  and  vaporized  by  the  applica- 
tion of  heat,  and  that  the  practical  infusibility  of  certain 
substances  is  due  to  our  limited  abilities  in  the  production 
of  heat. 

(a.)  Many  vapors  and  gases,  as  steam  and  sulphurous  anhydride 
(SO2,the  irrespirable  gas  formed  by  burning  sulphur), may  be  liquefied 
by  cold,  the  withdrawal  of  heat.  The  process  is  one  of  subtraction. 
A  still  further  diminution  of  the  heat  force  would,  in  many  cases, 
lead  to  a  solidifying  of  the  liquid.  It  is  probable  that  all  gases 
might  be  liquefied  and  all  liquids  solidified,  if  we  had  the  power  of 
unlimited  withdrawal  of  heat.  In  fact,  it  is  claimed  that  the  last  of 
the  "  permanent  gases"  has  been  liquefied  already. 

60.  What    is    a   Fluid?— A  fluid  is    a   body 
whose    molecules    easily    change    their    relative 
positions. 

The  term  comprehends  liquids,  gases,  and  vapors. 

61.  Optional  Definitions.— (1.)  A  body  possess- 
ing any  degree  of  elasticity  of  form  (§  45)  is  a  solid ;   a 
body  that  possesses  no  elasticity  of  form  is  a  fluid. 

(2.)  A  body  that  can  exist  in  equilibrium  under  the 
action  of  a  pressure  that  is  not  uniform  in  all  directions 
is  a  solid ;  a  body  that  cannot  exist  in  equilibrium  under 
such  conditions  is  a  fluid. 

(3.)  A  fluid  that  can  expand  indefinitely  so  as  to  fill  any 
vessel,  however  large,  is  an  aeriform  body ;  a  fluid,  a  small 
portion  of  which,  when  placed  in  a  large  vessel,  does  not 
expand  at  once  so  as  to  fill  the  vessel,  but  remains  col- 
lected at  the  bottom,  is  a  liquid. 


24  THE  THREE  CONDITIONS   OF  MATTER. 

62.  Test  Questions.— What  is  the  one  character- 
istic difference  between  a  solid  and  a  liquid  ?  Between  a 
liquid  and  a  gas  ?  Between  a  gas  and  a  vapor  ?  Between 
a  fluid  and  a  solid  ?  Into  what  two  classes  may  these 
three  physical  conditions  of  matter  be  divided,  reference 
being  made  only  to  ease  or  difficulty  of  a  change  of  rela- 
tive position  of  the  molecules  ? 

Note.—  Recent  experiments  with  electric  discharges  in  high  vacu- 
ums [§§  290 ;  371  (31)]  have  yielded  remarkable  results  which  are 
held,  by  some,  to  show  the  existence  of  a  fourth  condition  of  matter. 
Formatter  in  this  "  ultra-gaseous  "  state,  the  name  "  Radiant  mat- 
ter "  has  been  proposed. 

Recapitulation. — To  be  reproduced,  upon  paper  or 
the  blackboard,  by  each  pupil. 


MATTER 


SOLIDS. 

Molecules  change 
their  relative  po- 
sitions with  diffi- 
culty. 


FLUIDS. 

Molecules  change 
their  relative  po- 
sitions easily. 


LIQUIDS, 

Molecules  cling   to- 
gether feebly. 


AERIFORM   BODIES. 
Molecules    tend    to 
separate. 


GASES  ;     ordinarily 
aeriform. 

VAPORS  ;  ordinarily 
liquid  or  solid. 


DYNAMICS.-FORCE  AND   MOTION.— GRAVITATION.— 

FALLING    BODIES.— THE    PENDULUM.— 

ENERGY. 


ECTJON  I. 


\. 

FORCE    AND    MOTIO  N. 

63.  Dynamics. — Dynamics  is  that   branch  of 
physics  which  treats  of  forces  and  their  effects. 

These  effects  may  be  of  two  kinds. 

(a.)  The  forces  employed  may  be  counterbalanced.  If  they  thus 
act  upon  a  body  at  rest,  that  body  will  remain  at  rest ;  if  they  act 
upon  a  body  in  motion,  the  motion  will  not  be  changed  thereby. 
The  branch  of  dynamics  that  treats  of  forces  thus  balanced  is  called 
Static*. 

(&.)  The  forces  employed  may  act  against  the  inertia  of  matter 
(§  38),  and  produce  motion  or  change  of  motion.  The  branch  of 
dynamics  that  treats  of  forces  thus  used  is  called  Kinetics.  If  we 
have  a  problem  relating  to  the  forces  that  may  produce  equilibrium 
in  a  lever,  as  in  the  act  of  weighing  goods,  it  is  a  static  problem  ; 
if  a  problem  refer  to  the  velocity  of  a  falling  body,  or  the  amount 
of  work  that  may  be  done  by  the  uncoiling  of  a  watch-spring,  it  is 
a  kinetic  problem. 

Note. — No  attempt  will  be  made  to  maintain  the  distinction  be- 
tween the  static  and  kinetic  effects  of  forces. 

64.  What  is  Force?— The  word  force  is  difficult 
of  satisfactory  definition.     As  generally  used,  it  signifies 

2 


26  FORCE  AND  MOTION. 

any  cause  that  tends  to  produce,  change,  or  destroy 
motion. 

It  follows  from  inertia  that  bodies  are  incapable  of 
changing  their  condition  of  rest  or  motion.  Any  cause 
capable  of  producing  a  tendency  to  change  either  of  these 
conditions,  is  called  a  force. 

(a.)  We  say  that  the  tendency  of  a  force  acting  on  a  body  at  rest 
is  to  move  it.  Motion  will  be  produced  if  the  body  is  free  to  move. 
This  motion  may  be  prevented  by  the  simultaneous  action  of  another 
force  or  of  other  forces.  Or  the  body  may  be  fixed  so  that  a  given 
pull  or  pressure,  *.  e.,  the  application  of  force,  will  produce  no 
motion.  In  this  case,  opposing  forces  are  called  into  action  as  soon 
as  the  given  force  begins  to  act,  and  thus  the  new  force  is  neutralized. 
For  instance,  a  small  boy  may  exert  all  of  his  muscular  power  upon 
a  large  stone  and  not  lift  it  at  all.  The  force  employed  produces  no 
motion.  The  attraction  between  the  earth  and  the  stone  (§  33)  is  a 
force  acting  in  a  downward  vertical  direction.  This  force  is  exactly 
balanced  by  the  upward  pressure  of  the  supporting  earth  or  floor 
(§  93).  If  the  stone  weighs  two  hundred  pounds  and  the  boy  lifts 
fifty  pounds,  the  supporting  body  exerts  an  upward  pressure  of  only 
one  hundred  and  fifty  pounds.  One  quarter  of  the  weight  of  the 
stone  or  a  downward  force  of  fifty  pounds  is  thus  liberated  or  called 
into  play  by  the  very  act  of  lifting  with  a  force  of  fifty  pounds. 
Hence  no  motion  is  produced,  because  an  opposing  force  is  called 
into  action  as  soon  as  the  given  force  begins  to  act,  and  thus  the 
new  force  is  neutralized. 

(&.)  In  this  case,  the  greatest  opposing  force  that  can  be  set  free 
or  called  into  play  is  a  force  of  two  hundred  pounds,  the  full  weight 
of  the  stone.  If,  therefore,  the  stone  be  lifted  with  a  force  of  more 
than  two  hundred  pounds,  the  new  force  can  not  be  wholly  neutral- 
ized and  motion  will  take  place.  If  there  be  no  opposing  force  to  be 
thus  called  into  action,  or,  in  other  words,  if  the  body  be  free  to 
move,  the  smallest  conceivable  force  will  overcome  the  inertia  and 
produce  motion. 

65.  Elements  of  a  Force.— In  treating  of  forces, 
we  have  to  consider  three  things : 

(1.)  The  point  of  application,  or  the  point  at  which 
the  force  acts. 


FORCE  AND  MOTION.  27 

(2.)  The  direction,  or  the  right  line  along  which  it 
tends  to  move  the  point  of  application. 

(3.)  The  magnitude  or  value  when  compared  with  a 
given  standard,  or  the  relative  rate  at  which  it  is 
able  to  produce  motion  in  a  body  free  to  move. 

66.  Measurement  of  Forces.— It  frequently  is 
desirable  to  compare  the  magnitudes  of  two  or  more  forces. 
That  they  may  be  compared,  they  must  be  measured ;  that 
they  may  be  measured,  a  standard  of  measure  or  unit  of 
force  is  necessary.     When  this  unit  has  been  determined 
upon,  the  value  of  any  given  force  is  designated  by  a  nu- 
merical reference  to  the  unit,  just  as  we  refer  quantities  of 
weight  to  the  kilogram  or  pound,  or  quantities  of  distance 
to  the  meter  or  yard.     The  magnitude  of  any  force  may  be 
measured  by  either  of  two  units,  which  we  shall  now  con- 
sider. 

67.  The  Gravity  Unit.— The  given  force  may  be 
measured  by  comparing  it  with  the  gravity  of  some  known 
quantity  or  mass  of  matter.     This  is  a  very  simple  and 
convenient  way,  and  often  answers  every  purpose.     TJie 
gravity  unit  of  force  is  the  gravity  of  any  unit  of 
mass.     This  unit  of  mass  may  be  a   gram,  kilogram, 
pound,  or  ton,  or  any  other  unit  that  may  be  more  con- 
venient under  the  circumstances. 

(a.)  A  force  is  said  to  be  a  force  of  100  kilograms  when  it  may  be 
replaced  by  the  action  of  a  weight  of  100  kilograms.  The  pressure 
of  steam  in  a  boiler  is  generally  measured,  at  present,  in  pounds  per 
square  inch,  that  is,  by  determining  the  number  of  pounds  with 
which  it  would  be  necessary  to  load  down  a  movable  horizontal 
square  inch  at  the  top  of  the  boiler  in  order  to  keep  it  in  place 
against  the  pressure  of  the  steam.  A  cord  or  rope  may  be  pulled 
with  a  certain  force.  This  force  is  measured  by  finding  out  how 


28  FORCE  AND  MOTION. 

many  pounds  suspended  by  the  cord  or  rope  would  give  it  an  equal 
pull  or  tension. 

(&.)  As  we  shall  see,  the  force  of  gravity  exerted  upon  a  given 
mass  is  variable.  A  given  piece  of  iron  would  weigh  more  at  the 
poles  than  at  the  equator.  Other  variations  in  the  force  of  gravity 
are  known.  When,  therefore,  scientific  accuracy  is  required,  it  will 
not  suffice  to  speak  of  a  force  of  ten  pounds,  but  we  may  speak  of  a 
force  of  ten  pounds  at  the  sea-level  at  New  York  City.  The  neces- 
sary corrections  may  then  be  made.  But  for  ordinary  purposes, 
these  details  may  be  disregarded. 

68.  The  Absolute   Unit. — TIxe  absolute  or  ki- 
netic unit  of  force  is  the  force  that,  acting  for 
unit  of   time  upon  unit  of  mass,  will  produce 
unit  of  velocity. 

If  we  adopt  the  common  units,  the  kinetic  unit  of  force 
is  the  force  that,  applied  to  one  pound  of  matter  for  one 
second,  will  produce  a  velocity  of  one  foot  per  second. 

(a.)  In  all  kinetic  questions  the  kinetic  unit  is  far  more  convenient. 
Gravity  units  may  easily  be  changed  to  kinetic  units.  At  the  lati- 
tude of  New  York,  the  force  of  gravity  acting  upon  one  pound  of 
matter  left  free  to  fall  will  give  it  a  velocity  of  32.13  ft.  per  second 
for  every  second  that  it  acts.  Consequently,  at  such  latitudes,  the 
gravity  unit  is  equal  to  32.16  kinetic  units. 

69.  The    Dyne. — Instead  of  using  a  unit  of  force 
based  upon  the  foot  and  pound,  scientific  men  are  coming 
to  use  a  similar  unit  based  upon  the  centimeter  and  gram. 
This  unit  has  recently  received  a  definite  name.     The 
dyne    is    the   force   which,   acting  for  one    second 
upon  a  mass  of  one  gram,  produces  a  velocity  of 
one  centimeter  per  second* 

(a.}  If  a  body  weighing  25  grams  acquires  in  one  second  a  velocity 
of  30  cm.  the  moving  force  was  750  dynes.  If  it  acquires  the  same 
velocity  in  2  seconds,  of  course  tlie  force  was  only  half  as  great,  or 
375  dynes. 

(&.)  The  several  units  based  upon  the  centimeter,  gram  and  second, 


FORCE  AND  MOTION.  29 

constitute  a  class  called  (from  the  initial  letters  of  tliese  words) 
C.  G.  S.  Units.    Thus  the  dyne  is  the  C.  G.  S.  unit  of  force. 

Note  to  the  Pupil. — We  have  been  speaking  of  unit  of  mass,  and 
you  have  probably  had  no  difficulty  in  understanding  that,  by  this 
term,  a  certain  definite  quantity  of  matter  is  meant.  This  certain 
quantity  may  be  any  quantity  that  we  agree  upon  as  a  unit  of 
measure.  In  this  country  we  have,  as  yet,  no  commonly  accepted 
unit  of  mass.  In  countries  where  the  metric  system  of  weights 
and  measures  is  used,  the  unit  of  mass  is  the  quantity  of  matter 
contained  in  one  cu.  cm.  of  pure  water  at  its  temperature  of  greatest 
density.  It  will  be  seen  that  this  definition  is  independent  of  gravity, 
and  that  it  holds  good  for  matter  anywhere.  The  quantity  of  matter 
in  the  unit  thus  defined  is  invariable,  while  the  gram,  which  is  its 
weight  (§  36),  is  variable.  But  notwithstanding  this,  at  any  given 
place,  weight  is  proportional  to  mass,  and  we,  therefore,  conveniently 
use  weight  as  a  means  of  estimating  mass.  We  speak  without  any 
considerable  ambiguity  of  a  pound  of  matter,  because  we  know  that 
a  mass  that  weighs  two  pounds  at  the  same  place  has  j  ust  twice  as 
much  matter  as  the  first,  which  we  may  take  as  a  convenient  unit  of 
mass. 

70.  Momentum. — The  momentum  of  a  body  is 
its  quantity  of  motion. 

Its  measure  is  the  product  of  the  numbers  representing 
the  mass  and  the  velocity. 

(a.}  One  tendency  of  force  is  to  produce  motion.  Two  units  of 
force  will  produce  twice  as  much  motion  as  one  unit.  This  doubled 
momentum  or  quantity  of  motion  may  exist  in  two  units  of  mass 
having  one  unit  of  velocity,  or  in  one  unit  of  mass  with  two  units  of 
velocity.  The  momentum  of  a  body  having  a  mass  of  20  pounds 
and  a  velocity  of  15  feet,  is  twice  as  great  as  that  of  a  body  having  a 
mass  of  5  pounds  and  a  velocity  of  30  ft.  The  momentum  of  the 
former  is  300 ;  that  of  the  latter,  150.  Momentum  has  reference 
only  to  force  and  inertia.  Therefore,  when  acting  upon  bodies  free 
to  move,  equal  forces  will  produce  equal  momenta  whether  the 
bodies  acted  upon  be  light  or  heavy.  The  unit  of  momentum  has  no 
definite  name. 

71.  Experiment.— Figure  6    represents  a  piece  of 
apparatus,  devised  by  Ritchie  of  Boston.     It  consists  of 


30 


FORCE  AND  MOTION. 


two  ball  pendulums,  one  of  which  weighs  twice  as  much 

as  the  other,  suspended  as 
represented.  The  heavier  ball 
contains  a  spring-hammer, 
which  is  held  back  by  a  thread. 
The  hammer  being  thus  held 
back,  and  the  smaller  ball 
resting  against  its  face,  the 
thread  is  burned,  a  blow  is 
struck,  and  an  equal  force  is 
exerted  upon  each  ball  (§§  72 
[3]  and  93).  The  smaller  ball 
will  move  twice  as  fast  and 
twice  as  far  as  the  larger  ball, 


FIG.  6. 


equal  forces  producing  equal  momenta. 
EXERCISES. 

1.  Find  the  momentum  of  a  500  Ib.  ball  moving  500  feet  a  second. 

2.  By  falling  a  certain  time,  a  200  Ib.  ball  lias  acquired  a  velocity 
of  321.6  ft.    What  is  its  momentum  ? 

8.  A  boat,  that  is  moving  at  the  rate  of  5  miles  an  hour,  weighs 
4  tons;  another,  that  is  moving  at  the  rate  of  10  miles  an  hour, 
weighs  2  tons.  How  do  their  momenta  compare? 

4.  What  is  meant  by  a  force  of  10  pounds  ?    To  how  many  kinetic 
units  is  it  equal  ? 

5.  A  stone  weighing  12  oz.  is  thrown  with  a  velocity  of  1320  ft. 
per  minute.     An  ounce  ball  is  shot  with  a  velocity  of  15  miles  per 
minute.    Find  the  ratio  between  their  momenta. 

6.  An  iceberg  of  50,000  tons  moves  with  a  velocity  of  2  miles  an 
hour  ;  an  avalanche  of  10,000  tons  of  snow  descends  with  a  velocity 
of  10  miles  an  hour.     Which  has  the  greater  momentum  ? 

7.  Two  bodies  weighing  respectively  23  and  40  pounds  have  equal 
momenta.     The  first  has  a  velocity  of  60  ft.  a  second  ;  what  is  the 
velocity  of  the  other  ? 

8.  Two  balls  have  equal  momenta.    .The  first  weighs  100  kilo- 


FORCE  AND  MOTION.  31 

grams  and  moves  with  a  velocity  of  20  meters  a  second.     The  other 
moves  with  a  velocity  of  500  meters  a  second.    What  is  its  weight  ? 

9.  A  force  of  1000  dynes  acts  on  a  certain  mass  for  one  second  and 
gives  it  a  velocity  of  20  cm.  per  second.      What  is  the  mass  in 
grams?  Ans.  50. 

10.  A  constant  force,  acting  on  a  mass  of  12  g.  for  one  second, 
gives  it  a  velocity  of  6  cm.  per  second.     Find  the  force  in  dynes. 

11.  A  force  of  490  dynes  acts  on  a  mass  of  70  g.  for  one  second. 
What  velocity  will  be  produced  ?  Ans.  7. 

12.  Two  bodies  start  from  a  condition  of  rest  and  move  towards 
each  other  under  the  influence  of  their  mutual  attraction  (§§  7  and 
98).     The  first  has  a  mass  of  1  g. ;  the  second,  a  mass  of  100 g.    The 
force  of  attraction  is  T^  dyne.     What  will  be  the  velocity  acquired 
by  each  during  one  second  ? 

72.  Laws  of  Motion. — The  following  propositions, 
known  as  Newton's  Laws  of  Motion,  are  so  important  and 
BO  famous  in  the  history  of  physical  science  that  they 
ought  to  be  remembered  by  every  student : 

(1.)  Every  ~body  continues  in  its  state  of  rest  or 
of  uniform  motion  in  a  straight  line 
unless  compelled  to  change  that  state  by 
an  external  force. 

(2.)  Every  motion  or  change  of  motion  is  in  the 
direction  of  the  force  impressed  and  is 
proportionate  to  it. 

(3.)  Action  and  reaction  are  equal  and  opposite 
in  direction. 

73.  The  First  Law.— The  first  law  of  motion  re- 
sults directly  from  inertia   (§  38).     It  is  impossible  to 
furnish  perfect  examples  of  this  law  because  all  things 
within  our  reach  or  observation  are  acted  upon  by  some 
external  force.     A  base-ball  when  once  set  in  motion  has 
no  power  to  stop  itself  (§  38,  a).     If  it  moved  in  obe- 


o-C  FORCE  AND  MOTION. 

dience  to  the  muscular  impulse  only,  its  motion  would  be 
in  a  straight  line ;  but  the  force  of  gravity  is  ever  active, 
and  constantly  turns  it  from  that  line,  and  forces  it  to 
move  in  a  graceful  curve  instead. 

74.  Centrifugal  Force.— Although  it  is  obviously 
impossible  to  give  any  direct  experimental  proof  of  the  first 


FIG.  7. 

law  of  motion,  we  see  many  illustrations  of  the  tendency 
of  moving  bodies  to  move  in  straight  lines  even  when 
forced  to  move  in  curved  lines.  A  curved  line  may  be 
considered  a  series  of  infinitely  small  straight  lines.  A 
body  moving  in  a  curve  has,  by  virtue  of  its  inertia,  a 
tendency  to  follow  the  prolongation  of  the  small  straight 
line  in  which  it  chances  to  be  moving.  Such  a  prolonga- 
tion becomes  a  tangent  to  the  curve,  to  move  in  which  a 
body  must  fly  further  from  the  centre.  This  tendency 


FORCE  AND  MOTION.  33 

of  matter  bo  move  in  a  straight  line,  and,  conse- 
quently, further  away  from  the  centre  around 
which  it  is  revolving,  is  called  Centrifugal  Force, 
from  the  Latin  words  which  mean  to  fly  from  the  centre. 
The  "laws"  of  this  "centrifugal  force"  may  be  studied 
or  illustrated  by  the  whirling-table  and  accompanying 
apparatus,  represented  in  Figure  7.  (See  §  77.) 

75.  Caution. — It  is  to  be  noticed  that  this  so-called 
"  Centrifugal  Force "  is  not  a  force  at  all.    It  is 
simply  inertia  manifested  under  special  conditions.    It  is 
one  of  the  universal  properties  of  matter  by  virtue  of 
which  the  body  shows  a  decided  determination  to  obey 
the  first  law  of  motion.    The  facts  of  the  case  are  the 
direct  opposite  of  those  implied  by  this  ill-chosen  name. 
Take  a  common  sling,  for  instance.   The  implication  made 
by  the  term,  "  Centrifugal  Force,"  is  that  the  pebble  in  the 
revolving  sling  has  a  natural  tendency  to  continue  moving 
in  a  circle,  and  that  some  external  force  is  necessary  to 
overcome  that  tendency.     The  truth  is  that  the  natural 
tendency  of  the  pebble  is  to  move  in  a  straight  line,  and  the 
o"nly  reason  that  it  does  not  thus  move  is  that  it  is  continu- 
ally forced  from  its  natural  path  by  the  pull  of  the  string. 
As  soon  as  this  external  force  is  removed,  by  intent  or 
accident,  away  flies  the  stone  in  obedience  to  its  own  law- 
abiding  tendencies. 

76.  Simply  Suggestive.— Examples  and  effects  of 
this  so-called  centrifugal  force  may  be  suggested  as  follows: 
Wagon  turning  a  corner,  railway  curves,  water  flying  from 
a  revolving  grindstone,  broken  fly-wheels,  spheroidal  form 
of  the  earth,  erosion  of  river-beds,  a  pail  of  water  whirled 
in  a  vertical  circle,  the  inward  leaning  of  the  circus-horse 
and  rider,  the  centrifugal  drying  apparatus  of  the  laundry 


34  FORCE  AND  MOTION. 

or  sugar  refinery,  difference  between  polar  and  equatorial 
weights  of  a  given  mass,  etc. 

77.  Note. — Mathematical    formulae    for   measuring    the    force 
necessary  to  overcome  this  tendency  of  matter  to  move  away  from 
the  centre  around  which  it  may  be  revolving,  or,  as  it  is  generally 
expressed,  for  measuring  the  centrifugal  force,  may  be  found  in  the 
Appendix.    It  is  sufficient  here  to  mention  that  this  force  varies 
directly  as  the  mass  and  as  the  square  of  the  velocity,  the  radius 
remaining  the  same  ;   doubling  the  mass  doubles  the  force  needed, 
but  doubling  the  velocity  quadruples  the  needed  restraining  force. 

78.  The  Second  Law. — The  second  law  of  motion 
is  sometimes  given  as  follows:   A  given  force  will  pro- 
duce the  same  effect  whether  the  body  on  which  it 
acts  is  in  motion  or  at  rest ;  whether  it  is  acted  on 
by  that  force  alone  or  by  others  at  the  same  time. 

(a. )  Many  attempts  have  been  made  to  show  that  these  are  only 
two  ways  of  stating  the  same  proposition  ;  most  of  them  are  more 
perplexing  than  profitable.  In  the  law  as  given  by  Newton  (§  72), 
the  word  motion  is  doubtless  used  in  the  sense  of  momentum.  If  the 
substitution  of  "  momentum  "  for  "  motion  "  makes  the  reconciliation 
any  easier,  no  objection  can  be  made  to  the  substitution. 

79.  Resultant   Motion. — Motion   produced   by 
the  joint  action  of  two  or  more  forces  is  called 
resultant  motion. 

The  point  of  application,  direction,  and  magnitude  of 
each  of  the  acting  forces  being  given,  the  direction  and 
magnitude  of  the  resultant  force  are  found  by  a  method 
known  as  the  composition  of  forces. 

80.  Composition  of  Forces.— Under  composi- 
tion of  forces,  three  cases  may  arise  : 

(1.)  Wlien  the  given  forces  act  in  the  same  direc- 
tion. The  resultant  is  then  the  sum  of  the  given 
forces.  Example  :  Rowing  a  boat  down  stream. 


FORCE  AND  MOTION.  35 

(2.)  W^^en  the  given  forces  act  in  opposite  di- 
rections. The  resultant  is  then  the  difference 
between  the  given  forces.  Motion  will  be  pro- 
duced in  the  direction  of  the  greater  force.  Ex- 
ample :  Rowing  a  boat  up  stream. 

(3.)  When  the  given  forces  act  at  an  angle.  The  re- 
sultant is  then  ascertained  by  the  parallelogram  of 
forces.  Example :  Rowing  a  boat  across  a  stream. 

81.  Graphic   Representation   of  Forces. — 

Forces  may  le  represented  by  lines,  the  point  of 
application  determining  one  end  of  the  line,  the  direc- 
tion of  the  force  determining  the  direction  of  the  line, 
and  the  magnitude  of  the  force  determining  the  length 
of  the  line. 

(a.}  It  will  be  noticed  that  these  three  elements  of  a  force  (§  65) 
are  the  ones  that  precisely  define  a  line.  By  drawing  the  line  as 
above  indicated,  the  units  of  force  being  numerically  equal  to  the 
units  of  length,  we  have  a  complete  graphic  representation  of  the 
given  force.  The  unit  of  length  adopted  in  any  such  representation 

may  be  determined  by  convenience; 

A.  but  the  scale  once  determined,  it 

must  be  adhered  to  throughout  the 
problem.  Thus  the  diagram  rep- 
resents two  forces  applied  to  the 
point  B.  These  forces  act  at  right 
angles  to  each  other.  The  arrow- 
v  J  heads  indicate  that  the  forces  rep 


FIG.  8.  resented  act  from  B  toward  A  and 

C  respectively.      The   force    that 

acts  in  the  direction  BA  being  20  pounds  and  the  force  acting  in  the 
direction  BC  being  40  pounds,  the  line  BA  must  be  one-half  as 
long  as  BC.  The  scale  adopted  being  1  mm.  to  the  pound,  the 
smaller  force  will  be  represented  by  a  line  2  cm.  long,  and  the  greater 
force  by  a  line  4  cm.  long. 

(&.)  The  graphic  determination  or  representation  of  the  resultant 
in  the  first  two  cases  under  the  "  Composition  of  Forces "  is  too 
simple  to  need  any  explanation. 


36  FORCE  AND  MOTION. 

82.  Parallelogram  of  Forces. — In  the  diagram, 
let  AB  and  AC  represent 

O- 

two  forces  acting  upon  the 
point  A.  Draw  the  two 
dotted  lines  to  complete  the 
parallelogram.  From  A,  the 
point  of  application,  draw 
the  diagonal  AD.  This 
diagonal  will  be  a  complete  graphic  representa- 
tion of  the  resultant.  In  such  cases  the  two  given 
forces  are  called  components.  The  resultant  of  any  two 
components  may  always  be  determined  in  this  way.  If 
two  forces,  such  as  those  represented  in  the  diagram,  act 
simultaneously  upon  a  body  at  A,  that  body  will  move 
over  the  path  represented  by  AD,  and  come  to  rest  at  D. 

(a.)  Suppose  that  instead  of  acting  simultaneously,  these  forces 
act  successively.  If  AC  act  first  for  a  given  time,  it  would  move  the 
body  to  C.  If  then  the  other  force  act  for  an  equal  time  it  would 
move  it  to  the  right  a  distance  represented  by  AB  or  its  equal  CD, 
and  the  body  be  left  at  D  as  before.  If  the  force  represented  by  AB 
acted  first  and  the  force  represented  by  AC  then  acted  for  an  equal 
time,  the  body  would  evidently  be  left  at  D.  Thus  we  see  that  these 
two  forces  produce  the  same  effect  whether  they  act  simultaneously 
or  successively. 

83.  Experimental    Verification.— This   prin- 
ciple of  the  parallelogram  of  forces  may  be  verified  by 
the  apparatus  represented  in  Fig.  10.      ABCD  is  a  very 
light  wooden  frame,  jointed  so  as  to  allow  motion  at  its 
four  corners.    The  lengths  of  opposite  sides  are  equal ;  the 
lengths  of  adjacent  sides  are  in  the  ratio  of  two  to  three. 
From  the  corners  B  and  C,  light,  flexible  silk  cords  pass 
over  the  pulleys  M  and  N,  and  carry  weights,  W  and  w, 
of  90  and  60  ounces  respectively,  the  ratio  between  the 


FORCE  AND  MOTION. 


37 


FIG.  10. 

weights  being  the  same  as  the  ratio  between  the  corres- 
ponding adjacent  sides  of  the  wooden  parallelogram.  A 
weight  of  120  ounces  is  hung  from  the  corner  A.  When 
the  wooden  frame  comes  to  rest  it  will  be  found  that  the 
sides  AB  and  AC  lie  in  the  direction  of  the  cords  which 
form  their  prolongations.  These  sides  AB  and  AC  are 
accurate  graphic  representations  of  the  two  forces  acting 
upon  the  point  A.  It  will  be  further  found  that  the 
diagonal  AD  is  vertical  and  twice  as  long  as  the  side  AC. 
Since  the  side  AC  represents  a  force  of  60  ounces,  AD  will 
represent  a  force  of  twice  60  ounces  or  120  ounces.  We 
thus  see  that  AD  fairly  represents  the  resultant  of  the 
two  forces  due  to  the  gravity  of  W  and  w,  for  this  result' 


38  FORCE  AND  MOTION. 

ant  is  equal,  and  opposite  to  the  vertical  force  which  is 
due  to  the  gravity  of  V,  and  this  balances  the  forces  repre- 
sented by  AB  and  AC.  Results  equally  satisfactory  will 
be  secured  as  long  as  AB  :  AC  ::  W  :  w. 

84.  A   Substitute. — Very  satisfactory  results  may 
be  had  by  simpler  apparatus.     Let  H 

and  K  represent  two  pulleys  that  work 
with  very  little  friction.    Fix  them  to  a     _,,.          /t " /i 
vertical    board.      The    blackboard    will     ®"v\/  [/ 
answer  well  if  the  pulleys  can  be  at- 
tached without  injury.    Three  silk  cords 
are  knotted  together  at  0  ;  two  of  them 
pass  over  the  pulleys;   the  three  cords 
carry  weights,  P,  Q,  and  R,  as  shown  in  FIG.  n. 

the  figure.  R  must  be  less  than  the 
sum  of  P  and  Q.  When  the  apparatus  has  come  to  rest, 
take  the  points  A  and  B  so  that  AO  :  BO  : :  P  :  Q.  Com- 
plete the  parallelogram  AOBD  by  drawing  lines  upon  the 
vertical  board.  Draw  the  diagonal  OD.  It  will  be  found 
by  measurement  that  AO  :  OD  : :  P  :  R;  or  that  BO  :  OD 
: :  Q  :  R.  Either  equality  of  ratios  affords  the  verification 
sought. 

85.  Determination   of   the   Value   of   the 
Resultant. — With  a  carefully-constructed  diagram  (only 
half  of  the  parallelogram  need  be  actually  drawn)  the  re- 
sultant may  be  directly  measured  and  its  value  ascertained 
from  the  scale  adopted.    The  value  and  direction  of  the 
resultant  may  be  found  trigonometrically,  without  actual 
construction  of  the  diagram,  when  the  angle  between  the 
directions  of  the  components  is  known.     In  one  or  two 
cases,  however,  the  mathematical  solution  i3  easy  without 


FORCE  AND  MOTION.  39 

the  aid  of  trigonometrical  formulae.  When  the  com- 
ponents act  at  right  angles  to  each  other,  the  resultant  is 
the  hypothenuse  of  a  right-angled  triangle.  (See  Olney's 
Geometry,  paragraph  346.)  When  the  components  are 
equal  and  include  an  angle  of  120°,  the  resultant  divides 
the  parallelogram  into  two  equilateral  triangles.  It  is 
equal  to  either  component,  and  makes  with  either  an  angle 
of  60°.  (Let  the  pupil  draw  such  a  diagram.) 

86.  Equilibraiit. — A  force   whose*    effect    is   to 
balance  the    effects  of  the    several    components  is 
called  an  equilibrant.     It  is  numerically  equal  to  the 
resultant,  and  opposite  in  direction.     Thus  in  Fig.  10,  the 
gravity  of  the  weight  V  is  the  equilibrant  of  W  and  w\ 
it  is  equal  and  opposite  to  the  resultant  represented  by 
AD. 

87.  Triangle  of  Forces. — By  reference  to  Fig.  9, 
it  will  be  seen  that  if  AC  represent  the  magnitude  and 
direction  of  one  component,  and  CD  the  magnitude  and 
direction  of  the  other  component,  the  line  AD,  which 
completes  the  triangle,  will  represent  the   direction  and 
intensity  of  the  resultant.     Where  the  point  of  application 
need  not  be  represented,  this  method  of  finding  the  rela- 
tive magnitudes  and  directions  is  more  expeditious  than 
the  one  previously  given.    If  the  line  which  completes  the 
triangle  be  measured  from  D  to  A,  that  is  to  say,  in  the 
order  in  which  the  components  were  taken,  it  represents 
the  equilibrant ;   the  arrow-head  upon  AD  should  then 
be  turned  the  other  way.     If  this  line  be  measured  from 
A  to  D,  that  is,  in  the  reverse  order,  it  represents  the 
resultant. 


40 


FORCE  AND   MOTION. 


88.  Composition  of  More  than  Two 
Forces. — If  more  than  two  forces  act  upon  the  point  of 
application,  the  resultant  of  any  two  may  be  combined 
with  a  third,  their  resultant  with  a  fourth,  and  so  on. 
The  last  diagonal  will  represent  the  resultant  of  all  the 
given  forces.  Suppose  that  four 
forces  act  upon  the  point  A,  as 
represented  in  the  diagram.  By 
compounding  the  two  forces  AB 
and  AC,  we  get  the  partial  re- 
sultant, Ar;  by  compounding 
this  with  AD,  we  get  the  second 
partial  resultant,  Ar';  by  com- 
pounding  this  with  AE,  we  get 
the  resultant,  AR  . 


FIG.  12. 


89.  Polygon  of  Forces. — This  resultant  may  be 
more  easily  obtained  by  the  polygon  of  forces.  If  a  num- 
ber of  forces  be  in  equilibrium, 
they  may  be  graphically  repre- 
sented by  the  sides  of  a  closed 
polygon  taken  in  order.  If  the 
forces  are  not  in  equilibrium,  the 
lines  representing  them  in  magni- 
tude  and  direction  will  form  a 
figure  which  does  not  close.  The  line  that  completes  the 
figure  and  closes  the  polygon  will,  when  taken  in  the  same 
order,  indicated  by  the  arrow-head  at  x,  represent  the 
equilibrant ;  when  taken  in  the  opposite  order,  indicated 
by  the  arrow-head  at  z,  it  will  represent  the  resultant. 
This  will  be  evident  from  a  comparison  of  the  diagram  with 
the  one  preceding,  the  forces  compounded  being  the  same. 


FIG.  13. 


FORCE  AND   MOTION.  41 

9O.  Parallelepiped  of  Forces. — The  component 
forces  may  not  all  act  in  the 
same  plane,  but  the  method  of 
composition  is  still  the  same. 
In  the  particular  case  of  three 
such  forces  it  will  be  readily 
seen  that  the  resultant  of  the 
FlG  forces  AB,  AC,  and  AD  is  rep- 

resented by  AR,  the  diagonal 
of  the  parallelepiped  constructed  upon  the  lines  represent- 
ing these  forces. 


91.  Resolution  of  Forces.  —  ^e   operation  of 
finding  the  components  to  which  a  given  force  is 
equivalent  is  called  the  resolution  of  forces. 

It  is  the  converse  of  the  composition  of  forces.  Repre- 
sent the  given  force  by  a  line.  On  this  line  as  a  diagonal 
construct  a  parallelogram.  An  infinite  number  of  such 
parallelograms  may  be  constructed  with  a  given  diagonal. 
When  the  problem  is  to  resolve  or  decompose  the  given 
force  into  two  or  more  components  having  given  direction^ 
it  is  definite  —  only  one  construction  being  possible.  The 
sides  that  meet  at  the  point  of  application  will  represent 
the  component  forces. 

92.  Example  of  Resolution  of  Forces.—  As 

we.  proceed  we  shall  find  more  than  one  example  of  the 
resolution  of  forces.  A  single  one  will  answer  in  this 
place.  It  is  a  familiar  fact  that  a  sail-boat  may  move  in  a 
direction  widely  different  from  that  of  the  propelling  wind, 
and  that,  under  such  circumstances,  the  velocity  of  the 
boat  is  less  than  it  would  be  if  it  were  sailing  in  the  direc- 
tion of  the  wind.  The  force  due  to  the  pressure  of  the 


OF  THE 


42  FORCE  AND  MOTION. 

wind  is  twice  resolved,  and  only  one  of  the  components 
is  of  use  in  urging  the  boat  forward.  In  Figure  15, 
let  KL  represent  the  keel  of  the 
boat ;  BC,  the  position  of  the  sail ; 
and  ^.7?,  the  direction  and  intensity 
of  the  wind.  In  the  first  place, 
when  the  wind  strikes  the  sail  thus 
placed,  it  is  resolved  into  two  com- 
ponents— BC  parallel  to  the  sail,  and 
BD  perpendicular  to  the  sail.  It  is 
evident  that  the  first  of  these  is  of 
no  effect.  But  the  boat  does  not  move  in  the  direction  of 
BD,  which  is,  in  turn,  resolved  by  the  action  of  the  keel 
and  rudder  into  two  forces,  BL  in  the  direction  of  the 
keel,  and  BE  perpendicular  to  it.  The  first  of  these  pro- 
duces the  forward  movement  of  the  boat ;  the  second 
produces  a  lateral  pressure  or  tendency  to  drift,  which  is 
more  or  less  resisted  by  the  build  of  the  boat. 

93.  The  Third  Law.— Examples  of  the  third  law 
of-  motion  are  very   common.    When  we  strike  an  egg 
upon  a  table,  the  reaction  of  the  table  breaks  the  egg;  the 
action  of  the  egg  may  make  a  dent  in  the  table.    The  re- 
action of  the  air,  when  struck  by  the  wings  of  a  bird, 
supports  the  bird  if  the  action  be  greater  than  the  weight. 
The  oarsman  urges  the  water  backward  with  the  same 
force  that  he  urges  his  boat  forward.     In  springing  from 
a  boat  to  the  shore,  muscular  action  tends  to  drive  the 
boat  adrift ;  the  reaction,  to  put  the  passenger  ashore. 

94.  Reaction    in    Noil- elastic  Bodies.— The 

effects   of  action   and   reaction   are   modified  largely  by 
elasticity,  but  never  so  as  to  destroy  their  equality.    Hang 


FORCE  AND  NOTION. 


43 


two  clay  balls  of  equal  mass  by  strings  of  equal  lengths 

so  that  they  will  just  touch  each  other.     If  one  be  drawn 

aside  and  let  fall  against 

the  other,  both  will  move 

forward,  but  only  half  as 

far  as  the  first  would  had 

it  met  no  resistance.    The 

gain  of  momentum  by  the 

second  is  due  to  the  action 

of  the  first.      It  is  equal 

to  the  loss  of  momentum 

by  the  first,  which  loss  is 

due  to  the  reaction  of  the 

second. 

95.  Reaction     in 
Elastic    Bodies.  —  If 

two  ivory  balls,  which  are 
elastic,  be  similarly  placed, 
and    the    experiment    re- 
peated, it  will  be  found  FIG.  16. 
that  the  first  ball  will  give 

the  whole  of  its  motion  to  the  second  and  remain  still 
after  striking,  while  the  second  will  swing  as  far  as  the 
first  would  have  done  if  it  had  met  no  resistance.  In  this 
case,  as  in  the  former,  it  will  be  seen  that  the  first  ball 
loses  just  as  much  momentum  as  the  second  gains. 

96.  Reflected    Motion.— Reflected    motion    is 
the  motion  produced  by  the  reaction  of  a  surface 
when  struck  by  a  body,  either  the  surface,  or  the 
body,  or  both  being  elastic. 

A  ball  rebounding  from  the  wall  of  a  house,  or  from  the 


44  FORCE  AND  MOTION. 

cushion  of  a  billiard-table,   is  an  example   of  reflected 
motion. 

97.  Law  of  Reflected  Motion.— The  angle  in- 
cluded between  the  direction  of  the  moving  body  before  it 
strikes  the  reflecting  surface  and  a  perpendicular  to  that 
surface  drawn  from  the  point  of  contact,  is  called  the  angle 


of  incidence.  The  angle  between  the  direction  of  the 
moving  body  after  striking  and  the  perpendicular,  is  called 
the  angle  of  reflection.  TJie  angle  of  incidence  is 
equal  to  the  angle  of  reflection,  and  lies  in  the 
same  plane.  A  ball  shot  from  A  will  be  reflected  at  B 
back  to  Ot  making  the  angles  ABD  and  CBD  equal. 

EXERCISES.     (Answers  to  le  written.) 

1.  Represent  graphically  the  resultant  of  two  forces,  100  and  150 
pounds  respectively,  exerted  by  two  men  pulling  a  weight  in  the 
same  direction.    Determine  its  value. 

2.  In  similar  manner,  represent  the  resultant  of  the  same  forces 
when  the  men  pull  in  opposite  directions.     Determine  its  value. 

3.  Suppose  an  attempt  be  made  to  row  a  boat  at  the  rate  cf  four 
miles  an  hour  directly  across  a  stream  flowing  at  the  rate  cf  three 
miles  an  hour.     Determine  the  direction  and  velocity  of  the  boat. 

4.  A  ball  falls  64  feet  from  the  mast  of  a  moving  ship  to  the 
deck.     During  the  time  of  the  fall,  the  ship  moved  forward  24  ft. 
Represent  the  actual  path  of  the  ball.     Find  its  length. 

5.  A  sailor  climbs  a  mast  at  the  rate  of  3  ft.  a  second  ;  the  ship  is 


FORCE  AND  MOTION. 


45 


sailing  at  the  rate  of  12  ft.  a  second.    Over  what  space  does  he 
actually  move  during  20  seconds  ? 

6.  A  foot-ball  simultaneously  receives  three  horizontal  blows  ;  one 
from  the  north  having  a  force  of  10  pounds;  one  from  the  east  having 
a  force  of  15  pounds,  and  one  from  the  south-east  having  a  force 
of  804  kinetic  units.     Determine  the  direction  of  its  motion. 

7.  Why  does  a  cannon  recoil  or  a  shot-gun  "  kick  "  when  fired  ? 
Why  does  not  the  velocity  of  the  gun  equal  the  velocity  of  the  shot  ? 

8.  If  the  river  mentioned  in  the  third  problem  be  one  mile  wide, 
how  far  did  the  boat  move,  and  how  much  longer  did  it  take  to  cross 
than  if  the  water  had  been  still  ? 

9.  A  plank  12  feet  long  has  one  end  on  the  floor  and  the  other  end 
raised  0  feet.    A  50- pound  cask  is  being  rolled  up  the  plank.    Resolve 
the  gravity  of  the  cask  into  two  components,  one  perpendicular  to 
the  plank  to  indicate  the  plank's  upward  pressure,*  and  one  parallel 
to  the  plank  to  indicate  the  muscular  force  needed  to  hold  the  cask 
in  place.    Find  the  magnitude  of  this  needed  muscular  force. 

Recapitulation.— To  be  amplified  by  the  pupil  for 


review. 


f  ELEMENTS. 


MEASUREMENTS.        \  GRAVITY  UNIT. 

(   KINETIC  UNIT.   Dyne. 

"CENTIFUGAL." 

FORCE. 

i-!  : 

Components. 

Resultant. 

w 

GRAPHIC                [  COMPOSITION.  - 

REPRESENTATION. 

1  RESOLUTION. 

Equilibrant. 
Parallelogram. 
Triangle. 

<  - 

Polygon. 

25 

STATICS. 

Q 

KINETICS, 

MOMENTUM. 

NEWTON'S  LAWS. 

.MOTION. 

RESULTANT  MOTION. 

ACTION  AND  REACTION. 

REFLECTED  MOTION. 

46  GRA  VITA  TloN. 

.ECTION  II. 

GRAVITATION. 

98,  What  is  Gravitation? — Every  particle  of 
matter   in    the   universe    has   an    attraction  for 
every    other   particle.      This    attractive    force    is 
called  gravitation. 

99.  Three    Important    Facts.— In    respect   to 
gravitation,  three  important  facts  have  been  established  : 

(1.)  It  acts  instantaneously.  Light  and  electricity 
require  time  to  traverse  space ;  not  so  with  this 
force.  If  a  new  star  were  created  in  distant 
space,  its  light  might  not  reach  the  earth  for 
hundreds  or  thousands  of  years.  It  might  be  in- 
visible for  many  generations  to  come,  but  its  putt 
would  be  felt  by  the  earth  in  less  than  the  twink- 
ling of  an  eye. 

(2.)  It  is  unaffected  by  the  interposition  of  any 
substance.  During  an  eclipse  of  the  sun,  the 
moon  is  between  the  sun  and  the  earth.  But 
at  such  a  time,  the  sun  and  earth  attract  each 
other  with  the  same  force  that  they  do  at  other 
times. 

(3.)  It  is  independent  of  the  kind  of  matter,  but 
depends  upon  the  quantity  or  mass  and 
the  distance.  We  must  not  fall  into  the  error 
of  supposing  that  mass  means  size.  The  planet 
Jupiter  is  about  1300  times  as  large  as  the  earth, 
but  it  has  only  about  300  times  as  much  matter 
because  it  is  only  0.23  as  dense. 


GRAVITATION.  47 

100.  Laws  of  Gravitation.— (1.)    Gravitation 
varies  directly  as  the  mass. 

(2.)  Gravitation  varies  inversely  as  the  square 
of  the  distance  (between  the  centres  of  gravity.  §  107). 

For  example,  doubling  the  mass,  doubles  the  attraction ; 
doubling  the  distance,  quarters  the  attraction ;  doubling 
both  the  mass  and  distance  will  halve  the  attraction. 
Trebling  the  mass  will  multiply  the  attraction  by  three; 
trebling  the  distance  will  divide  the 'attraction  by  nine; 
trebling  both  the  mass  and  distance  will  divide  the  attrac- 

(3        1  \ 
3*~3/' 

101.  Equality    of     Attraction.  —  Tl%e    force 
exerted  by  one  body  upon  a  second  is  the  same 
as  that  exerted  by  the  second  upon  the  first. 

The  earth  draws  the  falling  apple  with  a  force  that  gives 
it  a  certain  momentum;  the  apple  draws  the  earth  with  an 
equal  force  which  gives  to  it  an  equal  momentum.  The 
momenta  are  equal ;  the  velocities  are  not.  Why  not  ? 

102.  Gravity. — The  most  familiar  illustration  of  grav- 
itation is  the  attraction  between  the  earth  and  bodies 
upon   or  near  its   surface.     This  particular  form  of 
gravitation  is  commonly  called  gravity;    its  measure  is 
weight;  its  direction  is  that  of  the  plumb-line,  vertical. 

103.  Weight.— Weight,   like  gravity,  the  force  of 
which  it  is  the  measure,  varies  directly  as  the  mass, 
and  inversely  as  the  square  of  the  distance.     This 
distance  is  to  be  measured  between  the  centres  of  gravity 
of  the  earth  and  of  the  body  weighed.     When  we  ascend 
from  the  surface  there  is  nothing  to  interfere  with  the 
working  of  this  law ;  but  when  we  descend  from  the  surface 


48  OR  A  VITATION. 

we  leave  behind  us  particles  of  matter  whose  attraction 
partly  counterbalances  that  of  the  rest  of  the  earth. 

104.  Ail    Example. — Consider  the  earth's  radius 
to  be  4,000  miles,  and  the  earth's  density  to  be  uniform. 
At  the  centre,  a  body,  whose  weight  at  the  surface  is 
100    pounds,    would   be    attracted    in    every    direction 
with  equal  force.     The  resultant  of  these  equal  and  oppo- 
site forces  would  be  zero,  and  the  body  would  have  no 
weight.     At  1,000  miles  from  the  centre,  one  fourth  of  the 
distance  to  the  surface,  it  would  weigh  25  pounds,  one- 
fourth  the  surface  weight ;  at  2,000  miles  from  the  centre, 
50  pounds  ;  at  3,000  miles  from  the  centre,  75  pounds ;  at 
4,000  miles  from  the  centre,  or  the  surface  distance,  it 
would  weigh  100  pounds  or  the  full  surface  weight.    If 
carried  up  still  further,  the  weight  will  decrease  according 
to  the  square  of  the  distance.    At  an  elevation  of  4,000 
miles  above  the  surface  (8,000  miles  from  the  centre)  it 
will  weigh  25  pounds,  or  one-fourth  the  surface  weight. 

105.  Law  of  Weight. — Bodies  weigh  most  at 
the  surface  of  the  eaHh.     Below  the  surface,  the 
weight  decreases  as  the  distance  to  the  centre  de- 
creases.   Above  the  surface,  the  weight  decreases  as 
the  square   of  the   distance   from    the    centre  in- 
creases. 

106.  Formulas    for    Gravity   Problems. — 

Representing  the  surface  weight  by  W  and  the  surface  dis- 
tance (4,000  miles)  by  D,  the  other  weight  by  w9  and  the 
other  distance  from  the  earth's  centre  by  d,  the  above  law 
may  be  algebraically  expressed  as  follows: 

Below  the  earth's  surface :    w  :  W  : :  d  :  D. 

Above  the  earth's  surface :    w  :  W  : :  D2 :  d2. 


GRAVITATION.  49 


EXERCISES. 

1.  How  far  below  the  surface  of  the  earth  will  a  ten-pound  ball 
weigh  only  four  pounds  ? 

Solution. 

Formula:  w  :  W ::  d  :  D. 

Substituting ;        4  :  10  : :  d  :  4000 
lQd= 16000 

d=1600  miles  from  centre. 
4000—1600=2400  miles  below  the  surface.— Ans. 

2.  What  would  a  body  weighing  550  Ibs.  on  the  surface  of  the 
earth  weigh  3,000  miles  below  the  surface  ?  Ans.  137£  Ibs. 

3.  Two  bodies  attract  each  other  with  a  certain  force  when  they 
are  75  m.  apart.     How  many  times  will  the  attraction  be  increased 
when  they  are  50  m.  apart  ?  Ans.  2\. 

4.  Given  three  balls.     The  first  weighs  6  Ibs.  and  is  25  ft.  distant 
from  the  third.     The  second  weighs  9  Ibs.  and  is  50  ft.  distant  from 
the  third,    (a)  Which  exerts  the  greater  force  upon  the  third? 
(&)   How  many  times  greater  ?  Ans.  f . 

5.  A  body  at  the  earth's  surface  weighs  900  pounds  ;  what  would 
it  weigh  8,000  miles  above  the  surface  ? 

6.  How  far  above  the  surface  of  the  earth  will  a  pound  avoirdupois 
weigh  only  an  ounce? 

7.  At  a  height  of   3,000  miles   above   the  surface  of  the  earth, 
what  would  be  the  difference  in  the  weights  of  a  man  weighing  200 
Ibs.  and  of  a  boy  weighing  100  Ibs.  ? 

8.  Find  the  weight  of  a  180  Ib.  ball  (a)  2,000  miles  above  the 
earth's  surface  ;  (6)  2,000  miles  below  the  surface. 

9.  (a)  Would  a  50  Ib.  cannon  ball  weigh  more  1,000  miles  above 
the  earth's  surface,  or  1,000  miles  below  it  ?    (&)  How  much  ? 

10.  If  the  moon  were  moved  to  three  times  its  present  distance 
from  the  earth,  what  would  be  the  effect  (a)  on  its  attraction  for 
the  earth  ?    (6)   On  the  earth's  attraction  for  it  ? 

11.  How  far  below  the  surface  of  the  earth  must  an  avoirdupois 
pound  weight  be  placed  in  order  to  weigh  one  ounce  ? 

12.  How  far  above  the  surface  of  the  earth  must  2,700  pounds  be 
placed  to  weigh  1,200  pounds  ?  Ans.  2,000  miles. 

107.  Centre  of  Gravity.— The  centre  of  grav- 
ity of  a  body  is  the  point  about  which  all  the 
matter  composing  the  body  may  be  balanced. 
3 


50 


GRAVITATION. 


The  force  of  gravity  tends  to  draw  every  particle  of 
matter  toward  the  centre  of  the  earth,  or  downward  in  a 

vertical  line.  We  may  therefore 
consider  the  effect  of  this  force 
upon  any  body  as  the  sum  of  an 
almost  infinite  number  of  paral- 
lel forces,  each  of  which  is  acting 
upon  one  of  the  molecules  of 
which  that  body  is  composed. 
We  may  also  consider  this  sum 
of  forces,  or  total  gravity,  as 
acting  upon  a  single  point,  just 
FIG.  18.  as  the  force  exerted  by  two 

horses  harnessed  to  a  whiffle- 

tree  is  equivalent  to  another  force  (resultant)  equal  to  the 
sum  of  the  forces  exerted  by  the  horses,  and  applied  at  a 
single  point  at  or  near  the  middle  of  the  whiffle-tree. 
This  single  point,  which  may  thus  be  regarded  as  the 

point  of  application  of  the 
force  of  gravity  acting  upon  a 
body,  is  called  the  centre  of 
gravity  of  that  body.  In  other 
words,  the  weight  of  a  body 
may  be  considered  as  concen- 
trated at  the  centre  of  gravity. 

1O8.  How  to  find  the 
Centre  of  Gravity.  —  In 

a  freely  moving  body,  the  cen- 
tre of  gravity  will  be  brought 
as  low  as  possible,  and  will, 
therefore,  lie  in  a  vertical  line 
FIG.  19.  drawn  through  the  point  of 


Of  THE 


-'i*  IVERSITT 
51 


GRAVITATION. 


support.    This  fact  affords  a  ready  means  of  determining 
the  centre  of  gravity  experimentally. 

Let  any  irregularly  shaped  body,  as  a  stone  or  chair,  be 
suspended  so  as  to  move  freely.  Drop  a  plumb-line  from 
the  point  of  suspension,  and  make  it  fast  or  mark  its  direc- 
tion. The  centre  of  gravity  will  lie  in  this  line.  From  a 
second  point,  not  in  the  line  already  determined,  suspend 
the  body  ;  let  fall  a  plumb-line  as  before.  The  centre  of 
gravity  will  lie  in  this  line  also.  But  to  lie  in  both  lines,  the 
centre  of  gravity  must  lie  at  their  intersection.  (Fig.  19.) 

1O9.  May  be  Outside  of  the  Body.—  The  cen- 
tre of  gravity  may  be  outside  of  the  matter  of  which,  a 
body  consists,  as  in  the  case  of  a  ring,  hollow  sphere,  box, 
or  cask.  The  same  fact  is  illustrated  by  the  "  balancer," 
represented  in  the  figure.  The  centre 
of  gravity  is  in  the  line  joining  the 
two  heavy  balls,  and  thus  under  the 
foot  of  the  waltzing  figure.  But  the 
point  wherever  found  will  have  the 
same  properties  as  if  it  lay  in  the  mass 
of  the  body.  In  a  freely  falling  body, 
no  matter  how  irregular  its  form,  or 
how  indescribable  the  curves  made  by 
any  of  its  projecting  parts,  the  line  of 
direction  in  which  the  centre  of  grav- 
ity or  point  of  application  moves  will 
be  a  vertical  line  (§  65  [2]  ). 

FIG.  20.  11O.  Equilibrium.  —  Inasmuch 

as  the  centre  of  gravity  is  the  point  at 

which  the  weight  of  a  body  is  concentrated,  when  the 

centre  of  gravity  is  supported,  the  whole  body  will 


52  GRA  VITA  TIOX. 

rest  in  a  state  of  equilibrium.  The  centre  of  gravity 
will  be  supported  when  it  coincides  with  the  point  of  sup- 
port, or  is  in  the  same  vertical  line  with  it. 

111.  Stable  Equilibrium.—  ^  body  supported 
in  such  a  way  that,  when  slightly  displaced  from 
its  position  of  equilibrium,  it  tends  to  return 
to  that  position,  is  said  to  be  in  stable  equili- 
brium. Such  a  displacement  raises  the  centre  of  grav- 
ity. Examples:  a  disc  supported  above  the  centre;  a 
semi-spherical  oil-can;  a  right  cone  placed  upon  its 
base ;  a  pendulum  or  plumb-line.  The  cavalry-man 
represented  in  Fig.  21,  is  in  stable  equilibrium,  and 
may  rock  up  and  down, 
balanced  upon  his  horse's 
hind  -  feet,  because  the 
heavy  ball  brings  the  cen- 
tre of  gravity  of  the  com- 
bined mass  below  the 
points  of  support.  The 
"balancer"  (Fig.  20)  af- 
fords another  example  of 
stable  equilibrium. 


5.  Unstable  Equi-  FlG  2~ 

librium. — A  body  sup- 
ported in  such  a  way  that,  when  slightly  displaced 
from  its  position  of  equilibrium,  it  tends  to  fall 
further  from  that  position,  is  said  to  be  in  unstable 
equilibrium.  Such  a  displacement  lowers  the  centre  of 
gravity.  The  body  will  not  come  to  rest  until  the  centre 
of  gravity  has  reached  the  lowest  possible  point,  when  it 
will  be  in  stable  equilibrium.  Examples:  A  disc  sup- 


GRAVITATION. 


53 


M 


ported  below  its  centre  ;  a  right  cone  placed  on  its  apex ; 
an  egg  standing  on  its  end ;  or  a  stick  balanced  upright 
upon  the  finger. 

113.  Neutral  Equilibrium. — A  'body  supported 
171    sucli    a    way    that,    when    displaced   from    its 
position  of  equilibrium,  it  tends  neither  to  return 
to  its  former  position  nor  to  fall  further  from  it, 
is  said  to  be  in  neutral  or  indifferent  equilibrium. 
Such  a  displacement  neither  raises  nor  lowers  the  centre 
of  gravity.    Examples :   A  disc  supported  at  its  centre ;   a 
sphere  resting  on  a  horizontal  surface  ;  a  right  cone  rest- 
ing on  its  side. 

(a.)  In  the  accompanying  figure  M,  N  and  0  represent  three  cones 

placed  respectively 
in  these  three  con- 
ditions of  equili- 
brium. The  letter 
g  shows  the  posi- 
tion of  the  centre 
of  gravity  in  each. 
If  a  body  have 
two  or  more  points 
IG*  22'  of  support  lying  in 

the  same  straight  line,  the  body  will  be  in  neutral,  stable  or  unstable 
equilibrium  according  as  the  centre  of  gravity  lies  in  this  line,  is 
directly  below  it  or  above  it. 

114.  Line  of  Direction. — A  vertical  line  drawn 
downward  from  the  centre  of  gravity  is  called  the 
line  of  direction.    As  we  have  seen,  it  represents  the 
direction  in  which  the  centre  of  gravity  would  move  if 
the  body  were  unsupported.    It  may  be  considered  as  a 
line  connecting  the  centre  of  gravity  of  the  given  body 
and  the  centre  of  the  earth. 

115.  The    Base. —  TJxe    side   on    ivhich    a   body 
rests  is  called   its  base.    If  the  body  be  supported  on 


54  GRA  VITA  TION. 

legs,  as  a  chair,  the  base  is  the  polygon  formed  by  joining 
the  points  of  support. 

116.  Stability.—  W7ien    the    line    of    direction 
falls  within  the  base,  the  body  stands  ;  when  with- 
out the  base,  the  body  falls. 

In  the  case  of  the  tower  represented  in  Fig.  23,  if  the 
upper  part  be  removed,  the  line  of  direction  will  be  as 
shown  by  the  left  hand  dotted  line.  It  falls  within  the 
base,  and  the  tower  stands.  When  the  upper  part  is  fast- 
ened to  the  tower,  the  line  of  direction  is  represented  by 
the  right  hand  dotted  line.  This  falls 
without  the  base,  and  the  tower  falls. 
The  stability  of  bodies  is  measured 
by  the  amount  of  work  necessary  to 
overturn  them.  This  depends  upon 
the  distance  that  it  is  necessary  to 
raise  the  centre  of  gravity  (equivalent 
to  raising  the  whole  body),  that  the 
line  of  direction  may  fall  without  the 
base.  When  the  body  rests  upon  a 
point,  as  does  the  sphere,  or  upon  a 
line,  as  does  the  cylinder,  a  very  slight 
force  is  sufficient  to  move  it,  no  elevation  of  the  centre  of 
gravity  being  necessary.  The  broader  the  base,  and  the 
lower  the  centre  of  gravity,  the  greater  the  stability. 

117.  Illustrations  of  Stability.— Let  the  figure 
represent  the  vertical  section  of  a  brick  placed  upon  its 
side,  its  position  of  greatest 

stability.     In  order  to  stand  f 
the  brick  upon  its  end,  g,  the 

centre  of  gravity  must  pass  a 

over  the  edge  c.    That  is  to  FIG.  24. 


GRAVITATION.  55 

say,  the  centre  of  gravity  must  be  raised  a  distance  equal 
to  the  difference  between  ga  and  gc,  or  the  distance  nc. 
But  to  lift  g  this  distance  is  the  same  as  to  lift  the  whole 
brick  vertically  a  distance  equal  to  ne.  Now  draw  similar 
figures  for  the  brick  when  placed  upon  its  edge  and  upon 
its  end.  In  each  case  make  gn  equal  to  ga,  and  see  that 
the  value  of  nc  decreases.  But  nc  represents  the  distance 
that  the  brick,  or  its  centre  of  gravity,  must  be  raised 
before  the  line  of  direction  can  fall  without  the  base,  and 
the  body  be  overturned.  To  lift  the  brick,  or  its  centre  of 
gravity,  a  small  distance  involves  less  work  than  to  lift  it 
a  greater  distance.  Therefore,  the  greater  the  value  of  nc, 
the  more  work  required  to  overturn  the  body,  or  the 
greater  its  stability.  But  this  greater  value  of  nc  evidently 
depends  upon  a  larger  base,  a  lower  position  for  the  centre 
of  gravity,  or  both. 


FIG.  25. 


(a.)  These  facts  explain  the  stability  of  leaning  towers  like  those 
of  Pisa  and  Bologna.  In  some  such  towers  the  centre  of  gravity 
is  lowered  by  using  heavy  materials  for  the  lower  part  and  light 
materials  for  the  upper  part  of  the  structure.  It  is  difficult  to  stand 
upon  one  foot  or  to  walk  upon  a  tight  rope  because  of  the  smallness 


56 


GRAVITATION. 


of  the  base.  A  porter  carrying  a  pack  is  obliged  to  lean  forward ; 
a  man  carrying  a  load  in  one  hand  is  obliged  to  lean  away  from  the 
load,  to  keep  the  common  centre  of  gravity  of  man  and  load  over 
the  base  formed  by  joining  the  extremities  of  his  feet.  Why  does  a 
person  stand  less  firmly  when  his  feet  are  parallel  and  close  together 
than  when  they  are  more  gracefully  placed  ?  Why  can  a  child  walk 
more  easily  with  a  cane  than  without  ?  Why  will  a  book  placed  on 
a  desk-lid  stay  there  while  a  marble  would  roll  off  ?  Why  is  a  ton 
of  stone  on  a  wagon  less  likely  to  upset  than  a  ton  of  hay  similarly 
placed? 

EXERCISES. 

Explanatory  Note. — The  first  problem  in  the  table  below  may  be 
read  as  follows :  What  will  be  the  weight  of  a  body  which  weighs 
1200  pounds  at  the  surface  of  the  earth,  when  placed  2000  miles 
below  the  surface  ?  When  placed  4000  miles  above  the  surface  ? 
(Radius  of  earth =4000  miles.)  All  of  the  measurements  are  from 
the  surface. 


NUMBER  OF 
PROBLEM. 

BELOW  SURFACE. 

AT  SURFACE. 

ABOVE  SURFACE. 

Pounds. 

Miles  from 
Surface. 

Pounds. 

Pounds. 

Miles  from 
Surface. 

1 

? 

2000 

1200 

? 

4000 

2 

800 

? 

1200 

533i 

? 

3 

? 

3000 

800 

? 

6000 

4 

? 

1000 

150 

? 

1000 

5 

100 

? 

400 

100 

\ 

6 

£53 

3000 

9 

? 

4000 

7 

? 

1600 

? 

32 

6000 

8 

12i 

? 

100 

25 

? 

9 

? 

3250 

480 

? 

2000 

10 

90 

? 

450 

50 

? 

11 

160 

f) 

256 

? 

12000 

12 

201.6 

2600 

? 

16 

? 

13 

256 

? 

? 

40.96 

16000 

14 

20250 

? 

324000 

9000 

? 

15 

? 

3200 

? 

1280 

9000 

FALLING   BODIES.  57 

Recapitulation. — In  this  section  we  have  considered 
Gravitation ;  Facts  concerning  it ;  its  Law ; 
Gravity;  Weight;  Law  of  Weight;  Centre 
of  Gravity;  Equilibrium  and  Stability  of 
Bodies. 


ECTfON  III. 


FALLI  NG    BODIES. 

118.  A  Constant  Force. — The  tendency  of  force 
is  generally  to  produce  motion.     Acting  on  a  given  mass 
for  a  given  time,  a  given  force  will  produce  a  certain 
velocity.    If  the  same  force  acts  on  the  same  mass  for 
twice  the  time  it  will  produce  a  double  velocity.    A  force 
which    thus    continues    to  act  uniformly    upon    a 
body,   even  after   the  body  has  begun   to  move,  is 
called  a  constant  force.    The  velocity  thus  produced 
is  called  a  uniformly  accelerated  velocity.     If  a  constant 
force  gives  a  body  a  velocity  of  10  feet  in  one  second,  it 
will  give  a  velocity  of  20  feet  in  two  seconds,  of  30  feet  in 
three  seconds,  and  so  on.     The  force  of  gravity  is  a  con- 
stant force  and  the  velocity  it  imparts  to  the  falling  body 
is  a  uniformly  accelerated  velocity. 

119.  Velocities    of    Falling    Bodies.— If    a 

feather  and  a  cent  be  dropped  from  the  same  height,  the 
cent  will  reach  the  ground  first.  This  is  not  because  the 
cent  is  heavier,  but  because  the  feather  meets  with  more 
resistance  from  the  air.  If  this  resistance  can  be  removed 
or  equalized,  they  will  fall  equal  distances  in  equal  times, 


58 


FALLING  BODIES. 


or  will  fall  with  the  same  velocity.  This  resistance  may 
be  avoided  by  trying  the  experi- 
ment in  a  glass  tube  from  which 
the  air  has  been  removed.  The  re~ 
sistance  may  be  nearly  equalized  by 
making  the  two  falling  bodies  of 
the  same  size  and  shape  but  of  dif- 
ferent weights.  Take  an  iron  and 
a  wooden  ball  of  the  same  size,  drop 
them  at  the  same  time  from  an 
upper  window,  and  notice  that  they 
will  strike  the  ground  at  sensibly 
the  same  time. 

12O.  Reason  of  this  Equal- 
ity.— The  cent  is  heavier  than  the 
feather  and  is  therefore  acted  upon 
by  a  greater  force.  The  iron  ball 
has  the  greater  weight,  which  shows 
that  it  is  acted  upon  by  a  greater 
force  than  the  wooden  ball.  But 
this  greater  force  has  to  move  a 
greater  mass,  has  to  do  more  work 
than  the  lesser  force.  For  the  greater  force  to  do  the 
greater  ivork  requires  as  much  time  as  for  the 
lesser  force  to  do  the  lesser  work.  The  working  force 
and  the  work  to  be  done  increase  in  the  same  ratio.  A 
regiment  will  march  a  mile  in  no  less  time  than  a  single 
soldier  would  do  it ;  a  thousand  molecules  can  fall  no  fur- 
ther in  a  second  than  a  single  molecule  can. 

121.  Galileo's  Device. — To  avoid  the  necessity 
for  great  heights,  and  the  interference  of  rapid  motion 
with  accurate  observations,  Galileo  used  an  inclined 


FIG.  26. 


FALLING  BODIES. 


59 


plane,  consisting  of  a  long  ruler  having  a  grooved  edge, 
down  which  a  heavy  ball  was  made  to  roll.  In  this  way 
he  reduced  the  velocity,  and  diminished  the  interfering 
resistance  of  the  atmosphere  without  otherwise  changing 
the  nature  of  the  motion. 
Let  AB  represent  a  plane  so 
inclined  that  the  velocity  of 
a  body  rolling  from  B  toward 
A  will  be  readily  observable. 
Let  C  be  a  heavy  ball.  The 
gravity  of  the  ball  may  be 
represented  by  the  vertical 
line  CD.  But  CD  may  be  resolved  into  CF,  which  repre- 
sents a  force  acting  perpendicular  to  the  plane  and  pro- 
ducing pressure  upon  it  but  no  motion  at  all,  and  CE, 
which  represents  a  force  acting  parallel  to  the  plane,  the 
only  force  of  any  effect  in  producing  motion.  It  may  be 
shown  geometrically  that 

EC  :  CD  ::  BG  :  BA.     (Olnetfs  Geometry,  Art.  341.) 

By  reducing,  therefore,  the  inclination  of  the  plane  we 
may  reduce  the  magnitude  of  the  motion  producing  com- 
ponent of  the  force  of  gravity  and  thus  reduce  the  velocity. 
This  will  not  affect  the  laws  of  the  motion,  that  motion 
being  changed  only  in  amount, 
not  at  all  in  character.  Jrl  \\u 


122.  Attwood's  Device. 

— For  the  purpose  of  lessening 
the  velocity  of  falling  bodies 
without  changing  the  character 
of  the  motion,  Mr.  Attwood 
devised  a  machine  which  has 


FIG.  28. 


FALLING   BODIES. 


taken  his  name.  Att- 
wood's  machine  consists 
essentially  of  a  wheel 
R,  about  six  inches 
in  diameter,  over  the 
grooved  edge  of  which 
are  balanced  two  equal 
weights,  suspended  by 
along  silk  thread,  which 
is  both  light  and  strong. 
The  axle  of  this  wheel 
is  supported  upon  the 
circumferences  of  four 
friction  wheels,  r,  r,  r,  r, 
for  greater  delicacy  oi 
motion.  As  the  thread 
is  so  light  that  its 
weight  may  be  disre- 
garded, it  is  evident 
that  the  weights  will  be 
in  equilibrium  whatever 
their  position. 

This  apparatus  is  sup- 
ported upon  a  wooden 
pillar,  seven  or  eight  feet 
high.  The  silk  cord 
carrying  K,  one  of  the 
weights,  passes  in  front 
of  a  graduated  rod 
which  carries  a  movable 
ring  B,  and  a  movable 
platform  A.  At  the  top 
of  the  pillar  is  a  plate  n, 


FALLING  BODIES.  63 

which  may  be  fastened  in  a  horizontal  position  for  the 
support  of  K  at  the  top  of  the  graduated  rod.  This  plate 
may  also  be  dropped  to  a  vertical  position,  thus  allowing  K, 
when  loaded,  to  fall.  A  clock,  with  a  pendulum  beating 
seconds,  serves  for  the  measurement  of  time,  and  the  drop- 
ping of  the  plate  at  the  top  of  the  pillar.  A  weight  or 
rider,  m,  is  to  be  placed  upon  K,  and  give  it  a  downward 
motion.  Levelling  screws  are  provided  by  means  of  which 
the  graduated  rod  may  be  made  vertical,  and  K  be  made 
to  pass  through  the  middle  of  B. 

(a.)  Suppose  that  K  and  K'  weigh  315  grams  each,  and  that  the 
rider  m  weighs  10  grams.  When  m  is  placed  upon  K  and  the  plate 
dropped  by  the  action  of  the  clock,  the  gravity  of  m  causes  the 
weights  to  move.  We  now  have  the  motion  of  640  grams  produced 
by  the  gravity  of  only  10  grams.  When  this  force  (gravity)  moves 
only  10  grams  it  will  give  it  a  certain  velocity.  When  the  same 
force  moves  640  grams  it  has  to  do  64  times  as  much  work,  and  can 
do  it  with  only  ^  the  velocity.  In  this  way  we  are  able  to  give  to 
K  and  m  any  velocity  of  fall  that  we  desire. 

123.  Experiments.— Arrange  the  apparatus  by  sup- 
porting K  and  m  upon  the  shelf  n.  As  the  hand  of  the 
clock  passes  a  certain  point  on  the  dial,  12  for  example, 
the  shelf  n  is  dropped  and  the  weights  begin  to  move.  By 
a  few  trials,  B  may  be  so  placed  that  at  the  end  of  one 
second  it  will  lift  m  from  K,  and  thus  show  how  far  the 
weights  fall  in  one  second.  Other  experiments  will  show 
how  many  such  spaces  they  will  fall  in  the  next  second  or 
in  two  seconds  ;  in  the  third  second  or  in  three  seconds ; 
in  the  fourth  second  or  in  four  seconds,  etc. 

Suppose  that  B  lifts  off  m  at  the  end  of  the  first  second. 
The  moving  force  being  no  longer  at  work,  inertia  will 
keep  K  moving  with  the  same  velocity  that  it  had  at  the 
end  of  the  first  second.  By  placing  A  so  that  K  will  reach 
it  at  the  end  of  the  second  second,  the  distance  AB  will 


62  FALLING  BODIES. 

indicate  the  velocity  with  which  K  was  moving  when  it 
passed  B  at  the  end  of  the  first  second.  In  a  similar  way 
the  velocity  at  the  end  of  the  second,  third,  or  fourth 
second  may  be  found. 

124.  Results. — Whatever  the  space  passed  over  in  the 
first  second  by  the  weights  or  the  ball,  it  will  be  found 
that  there  is  an  uniform  increase  of  velocity.   Galileo  found 
.that  if  the  plane  was  so  inclined  that  the  ball  would  roll 
one  foot  during  the  first  second,  it  would  roll  three  feet 
during  the  next  second,  five  feet  during  the  third,  and  so 
on,  the  common  difference  being  two  feet,  or  twice  the  dis- 
tance traversed  in  the  first  second. 

He  found  that  under  the  circumstances  supposed,  the 
ball  would  have  a  velocity  of  two  feet  at  the  end  of  the 
first  second,  of  four  feet  at  the  end  of  the  next,  of  six  feet 
at  the  end  of  the  third,  and  so  on,  the  increase  of  velocity 
during  the  first  second  being  the  same  as  the  increase 
during  any  subsequent  second. 

He  found  that,  under  the  circumstances  supposed,  the 
ball  would  pass  over  one  foot  during  one  second,  four  feet 
during  two  seconds,  and  nine  feet  during  three  seconds, 
and  so  on.  Similar  results  may  be  obtained  with  Att- 
wood's  machine. 

125.  Table  of  Results. — These  results  are  gener- 
alized in  the  following  table,  in  which  t  represents  any 
given  number  of  seconds: 


Number  of      i. 
Seconds. 
I 

Spaces  fallen  during 
each  Second. 
1 

Velocities  at  the  End 
of  each  Second. 
2  

Total  Nut 
Spaces  f 
1 

2 

.3  

4  

4 

3 

5 

6  , 

,  9 

4.. 

..7.. 

..8.. 

..1C 

etc.                      etc.      .                       etc.                         etc. 
t..  ...2t-l..  ...2t t2 


FALLING   BODIES.  OO 

.  Unimpeded  Fall. — By  transferring  matter 
from  K'  to  K,  the  velocity  with  which  the  weights  move 
will  be  increased.  When  all  of  K'  has  been  transferred  to 
K,  the  weights  will  fall,  in  this  latitude,  16.08  ft. 
or  J^.9  m.  during  the  first  second. 

If  the  plane  be  given  a  greater  inclination,  the  ball  will, 
of  course,  roll  more  rapidly  and  our  unit  of  space  will  in- 
crease from  one  foot,  as  supposed  thus  far,  to  two,  three, 
four  or  five  feet,  and  so  on,  but  the  number  of  such  spaces 
will  remain  as  indicated  in  the  table  above.  By  disre- 
garding the  resistance  of  the  air,  we  may  say  that  when 
the  plane  becomes  vertical,  the  body  becomes  a  freely 
falling  body.  Our  unit  of  space  has  now  become  16.08  ft. 
or  4.9  m.  It  will  fall  this  distance  during  the  first  second, 
three  times  this  distance  during  the  next  second,  five  times 
this  distance  during  the  third  second,  and  so  on. 

127.  Increment  of  Velocity.— During  the  first 
second  the  freely  falling  body  will  gain  a  velocity 
of  32.16  feet.      It  will  make  a  like  gain  of  velocity 
during  each  subsequent  second  of  its  fall.    This  distance 
is  therefore  called  the  increment  of  velocity  due  to  gravity, 
and  is  generally  represented  by  g  =  32.16  ft.  or  9.8  m. 

Note — This  value  must  not  be  forgotten. 

128.  Formulas  for  Falling  Bodies.— If  now  we 

represent  our  space  by  \g,  the  velocity  at  the  end  of  any 
second  by  v,  the  number  of  seconds  by  t,  the  spaces  fallen 
each  second  by  s,  and  the  total  space  fallen  through  by  S, 
we  shall  have  the  following  formulas  for  freely  falling 
bodies  : 

(1.)  v=gt  or  \g  x  2£. 

(2.)    a  =  te(2*_l). 
(3.)  S  =  %gt\ 


64  FALLING  BODIES. 

129.  Laws  of  Falling  Bodies.— These  formulas 
may  be  translated  into  ordinary  language  as  follows : 

(1.)  The  velocity  of  a  freely  falling  body  at  the  end  of 
any  second  of  its  descent  is  equal  to  32.16  ft.  (9.8  m.)  mul- 
tiplied by  the  number  of  the  second. 

(2.)  The  distance  traversed  by  a  freely  falling  body 
during  any  second  of  its  descent  is  equal  to  16.08  ft.  (4.9  m.) 
multiplied  by  one  less  than  twice  the  number  of  seconds. 

(3.)  The  distance  traversed  by  a  freely-falling  body 
during  any  number  of  seconds  is  equal  to  16.08  ft.  (4.9  m.) 
multiplied  by  the  square  of  the  number  of  seconds. 

130.  For  Bodies  Rolling  Down  an  Inclined 
Plane. — If  the  body  be  rolling  down  an  inclined  plane 
instead  of  freely  falling,  of  course  the  increment  of  velocity 
will  be  less  than  32.16  ft.     The  formulas  above  given  may 
be  made  applicable  by  multiplying  the  value  of  g  by  the 
ratio  between  the  height  and  length  of  the  plane. 

131.  Initial   Velocity  of  Falling  Bodies.— 

"We  have  been  considering  bodies  falling  from  a  state  of 
rest,  gravity  being  the  only  force  that  produced  the  motion. 
But  a  body  may  be  thrown  downward  as  well  as  dropped. 
In  such  a  case,  the  effect  of  the  throw  must  be  added  to 
the  effect  of  gravity.  It  becomes  an  illustration  of  the 
first  case  under  Composition  of  Forces  (§  80),  the  resultant 
being  the  sum  of  the  components.  If  a  body  be  thrown 
downward  with  an  initial  velocity  of  fifty  feet  per  second, 
the  formulas  will  become  v  =  gt  +  50 ;  s  =  J#  (2t—l) 
-f  50  ;  S  =  \£t*  +  50t. 

132.  Ascending  Bodies.— In  the  consideration  of 
ascending  bodies  we  have  the  direct  opposite  of  the  laws  of 
falling  bodies.     When  a  body  is  thrown  downward,  gravity 


FALLING  BODIES.  65 

increases  its  velocity  every  second  by  the  quantity  g. 
When  a  body  is  thrown  upward,  gravity  diminishes  its 
velocity  every  second  by  the  same  quantity.  Hence  the 
time  of  its  ascent  will  be  found  by  dividing  its  initial 
velocity  by  g.  The  initial  velocity  of  a  body  that 
can  rise  against  the  force  of  gravity  for  a  given 
number  of  seconds  is  the  same  as  the  final  velocity 
of  a  body  that  has  been  falling  for  tine  same 
number  of  seconds. 

(a.)  The  spaces  traversed  and  the  velocities  attained  during  suc- 
cessive seconds  will  be  the  same  in  the  ascent,  only  reversed  in 
order.  If  a  body  be  shot  upward  with  a  velocity  of  821.6  feet,  it 
will  rise  for  ten  seconds,  when  it  will  fall  for  ten  seconds.  The 
tenth  second  of  its  ascent  will  correspond  to  the  first  of  its  descent, 
i.  e.,  the  space  traversed  during  these  two  seconds  will  be  the  same ; 
the  eighth  second  of  the  ascent  will  correspond  to  the  third  of  its 
descent  ;  the  end  of  the  eighth  second  of  its  ascent  will  correspond 
to  the  end  of  the  second  second  of  its  descent. 

133.  Projectiles. — Every  projectile  is  acted  upon  by 
three  forces : 

(1.)  The  impulsive  force,  whatever  it  may  be. 
(2.)  The  force  of  gravity. 
(3.)  The  resistance  of  the  air. 

134.  Random   or  Range.— The  horizontal  dis- 
tance from   the   starting-point   of    a    projectile  to 
where  it  strikes   the  ground   is   called   its  random 
or  range.    In  Fig.  30,  the  line  GE  represents  the  ran- 
dom of  a  projectile   starting  from   F,  and  striking  the 
ground  at  E. 

135.  Path  of  a  Projectile.— The  path  of  a  pro- 
jectile is  a  curve,  the  resultant  of  the  three  forces  above 
mentioned.     Suppose  a  ball  to  be   thrown   horizontally. 
Its  impulsive  force  will  give  a  uniform  velocity,  and  may 


66 


FALLING   BODIES. 


-9 


be  represented  by  a  horizontal  line  divided  into  equal 
parts,  each  part  representing  a  space  equal  to  the  velocity. 

The  force  of  gravity  may  be 
represented  by  a  vertical  line 
divided  into  unequal  parts, 
representing  the  spaces  1, 3, 5,  7, 
etc.,  over  which  gravity  would 
move  it  in  successive  seconds. 
Constructing  the  parallelograms 
of  forces,  we  find  that  at  the 
16  end  of  the  first  second  the  ball 
will  be  at  A,  at  the  end  of  the 
next  second  at  B,  at  the  end  of 
the  third  at  C,  at  the  end  of  the 
25  fourth  at  D,  etc.  The  result- 
ant of  these  two  forces  is  a  curve 


FIG.  30. 


called  a  parabola.  It  will  be  seen  that,  in  a  case  like  this, 
the  range  GE  may  be  found  by  multiplying  the  velocity 
by  the  number  of  seconds  it  will  take  the  body  to  fall 
from  F  to  G.  The  resistance  of  the  air  modifies  the 
nature  of  the  curve  somewhat. 

136.  Time  of  a  Projectile. — From  the  second 
law  of  motion,  it  follows  that  the  ball  shot  horizontally 
will  reach  the  level  ground  in  the  same  time  as  if  it  had 
been  dropped ;  that  the  ball  shot  obliquely  upward  from  a 
horizontal  plain  will  reach  the  ground  in  twice  the  time 
required  to  fall  from  the  highest  point  reached.  These 
statements  may  be  easily  verified  by  experiment. 


FALLING   BODIES.  67 


EXERCISES. 

1.  What  will  be  the  velocity  of  a  body  after  it  has  fallen  4 
seconds  ? 

Solution :  v  =  gt. 

v  =  32.16x4. 

v  =  128.64.  Ans.  128.64  ft. 

i 

2.  A  body  falls  for  several  seconds  ;    during  one  it  passes  over 
530.64  feet ;  which  one  is  it? 

Solution  :  s  =  \g  (2t  -  1). 

530.64  =  16.08  x  (2t  -  1). 

33  =  2t  -  1. 

34  =  2t. 

17  =  t.  Ans.  17th  second. 

3.  A  body  was  projected  vertically  upward  with  a  velocity  =  96.48 
feet ;  how  high  did  it  rise  ? 

Solution  :  v  =  gt.    (See  §  132.) 

96.48  =  32.16*. 
3  =  t. 
S=\gt\ 
8  =  16.08  x  9. 
S  =  144.72.  Ans.  144.72  ft. 

4.  How  far  will  a  body  fall  during  the  third  second  of  its  fall  ? 

5.  How  far  will  a  body  fall  in  10  seconds  ?  Ans.  1608  ft. 

6.  How  far  in  |  second?  Ans.  4.02  ft. 

7.  How  far  will  a  body  fall  during  the  first  one  and  a  half  seconds 
of  its  fall  ? 

8.  How  far  in  12 1  seconds  ? 

9.  A  body  passed  over  787.93  feet  during  its  fall ;   what  was  the 
time  required  ?  Ans.  7  sec. 

10.  What  velocity  did  it  finally  obtain  ? 

11.  A  body  fell  during  15i  seconds  ;  give  its  final  velocity. 

12.  In  an  Att wood's  machine  the  weights  carried  by  the  thread 
are  6|  ounces  each.    The  friction  is  equivalent  to  a  weight  of  two 
ounces.    When  the  "  rider,"  which  weighs  one  ounce,  is  in  position, 
what  will  be  its  gain  in  velocity  per  second  ? 

13.  A  stone  is  thrown  horizontally  from  the  top   of  a  tower 
257.28  ft.  high  with  a  velocity  of  60  ft.  a  second.     Where  will  it 
strike  the  ground  ? 


68  FALLING  BODIES. 

14.  A  body  falls  freely  for  6  seconds.    What  is  the  space  trav- 
ersed during  the  last  2  seconds  of  its  fall  ? 

15.  A  body  is  thrown  directly  upward  with  a  velocity  of  80.4  ft. 
(a)  What  will  be  its  velocity  at  the  end  of  3  seconds,  and  (&)  in  what 
direction  will  it  be  moving? 

16.  In  Fig.  30,  what  is  represented  by  the  following  lines :  Fl  ? 
Fa?  Aa?  Fc?  Dd? 

17.  A  body  falls  357.28  ft.  in  4  seconds.    What  was  its  initial 
velocity  ? 

18.  A  ball  thrown  downward  with  a  velocity  of  35  ft.  per  second 
reaches  the  earth  in  12  \  seconds,      (a)  How  far  has  it  moved,  and 
(&)  what  is  its  final  veloc4ty  ? 

19.  (a)   How  long  will  a  ball  projected  upward  with  a  velocity  of 
3,216  ft.  continue  to  rise  ?      (6)   What  will  be  its  velocity  at  the 
end  of  the  fourth  second  ?    (c)    At  the  end  of  the  seventh  ? 

20.  A  ball  is  shot  from  a  gun  with  a  horizontal  velocity  of  1,000 
feet,  at  such  an  angle  that  the  highest  point  in  its  flight  =  257.28 
feet.     What  is  its  random?  A  us.  8000  ft. 

21.  A  body  was  projected  vertically  downward  with  a  velocity  of 
10  feet ;  it  was  5  seconds  falling.     Required  the  entire  space  passed 
over.  Ans.  452ft. 

22.  Required  the  final  velocity  of  the  same  body.    Ans.  170.8  ft. 

23.  A  body  was  5  seconds  rolling  down  an  inclined  plane  and 
passed  over  7  feet  during  the  first  second,      (a)  Give  the  entire 
space  passed  over,  and  (&)  the  final  velocity. 

24.  A  body  rolling  down  an  inclined  plane  has  at  the  end  of  the 
first  second  a  velocity  of  20  feet ;    (a)  what  space  would  it  pass 
over  in  10  seconds?     (&)  If  the  height  of  the  plane  was  800  ft., 
what  was  its  length  ?  Last  Ans.  1286.4  ft. 

25.  A  body  was  projected  vertically  upward  and  rose  1302.48  feet; 
give  (a)  the  time  required  for  its  ascent,  (&)  also  the  initial  velocity. 

26.  A  body  projected  vertically  downward  has  at  the  end  of  the 
seventh  second  a  velocity  of  235.12  feet ;  how  many  feet  will  it  have 
passed  over  during  the  first  4  seconds  ?  Ans.  297.28  ft. 

27.  A  body  falls  from  a  certain  height  ;    3  seconds  after  it  has 
started,  another  body  falls  from  the  height  of  787.92  feet ;    from 
what  height  must  the  first  fall  if  both  are  to  reach  the  ground  at 
the  same  instant  ?  Ans.  1608  ft. 

Recapitulation.— To  be  amplified  by  the  pupil  for 
review. 


THE   PENDULUM. 

f  ACTED   UPON    BY   A   CONSTANT   FORCE. 
RELATION    OF   WEIGHT  TO   VELOCITY. 


LAWS- 


ILLUSTRATIVE  (     Galileo's, 


Attwood's  . 

APPARATUS  Results  tabulated 


INCREMENT   OP    VELOCITY  WITH  j  Unimpeded. 
FALL.  (  Impeded. 

TAT  ^  Mathematical  symbols. 

IN  .........  , 


O 

^^  PJX  f  tt  hiwrshii  j     i  N     .  .  .  .  _     ..        "ii-vJi«  .--.-,,_. 

^  Ordinary  language. 


EFFECT   OF  INITIAL  VELOCITY. 


w 
RELATIONS  TO 


(  Ascending  bodies  ( 
-J       .  -J      h 

(Projectiles  .......  }gth 


ECTfON    IV. 


V. 

THE    PENDULU  M. 

137.  The   Simple  Pendulum. — A   simple  pen- 
dulum is  conceived  as  a  single  material  particle  sup- 
ported by  a  line  without  weight,  capable  of  oscillat- 
ing about  a  fixed  point.      Such   a"  pendulum  has   a 
theoretical  but  not  an  actual  existence,  and  has  been  con- 
ceived for  the  purpose  of  arriving  at  the  laws  of  the  com- 
pound pendulum. 

138.  The    Compound    Pendulum. — A    com- 
pound or  physical  pendulum  is  a  weight  so  suspended 
as  to  be  capable  of  oscillating  about  a  fixed-  point. 
The  compound  pendulum  appears  in  many  forms.     The 
most  common  form  consists  of  a  steel  rod,  thin  and  flexible 
at  the  top,  carrying  at  the  bottom  a  heavy  mass  of  met:il 
known  as  the  lob.     The  bob  is  sometimes  spherical  but 
generally  lenticular,  as  this  form  is  less  subject  to  resistance 
from  the  air. 


70 


THE  PENDULUM. 


FIG.  31. 


139.  Motion    of  the    Pendulum.— When    the 

supporting  thread  or  bar  is  vertical,  the  centre  of  gravity 
is  in  the  lowest  possible  position, 
and  the  pendulum  remains  at 
rest,  for  the  force  of  gravity  tends 
to  draw  it  downward  producing 
pressure  at  the  point  of  support, 
but  no  motion.  But  when  the 
pendulum  is  drawn  from  its  ver- 
tical position,  the  force  of  grav- 
ity, MG,  is  resolved  (§  91)  into 
two  components,  one  of  which, 
MC,  produces  pressure  at  the 
point  of  support,  while  the  other, 
MH,  acts  at  right  angles  to  it, 
producing  motion.  Gravity  there- 
fore draws  it  to  a  vertical  position,  when  inertia  carries  it 
beyond  until  it  is  stopped  and  drawn  back  again  by  grav- 
ity. It  thus  swings  to  and  fro  in  an  arc,  MNO. 

140.  Definitions. — The  motion  from  one  extremity 
of  this  arc  to  the  other  is  called  a  vibration  or  oscillation. 
The  time  occupied  in  moving  over  this  arc  is  called  the 
time  of  vibration  or  oscillation.    The  angle  measured  by 
this  arc  is  called  the  amplitude  of  vibration.     The  trip 
from   M    to  0  is   a  vibration;    the  angle  MAO   is   the 
amplitude  of  vibration. 

141.  Centre  of  Oscillation.— A  short  pendulum 
vibrates  more  rapidly  than  a  long  pendulum  ;    this  is  a 
familiar  fact.    It  is  evident,  then,  that  in  every  pendulum 
(not  simple)  the  parts  nearest  the  centre  of  suspension  tend 
to  move  faster  than  those  further  away,  and  force  them  to 


THE  PENDULUM.  71 

move  more  rapidly  than  they  otherwise  would.  On  the 
other  hand,  the  parts  furthest  from  the  centre  of  suspen- 
sion tend  to  move  more  slowly  than  those  nearer,  and  force 
these  to  retard  their  individual  rates  of  motion.  Between 
these  there  will  be  a  particle  moving,  of  its  own  accord, 
at  the  average  rate  of  all.  The  accelerating  tendency  of 
the  particles  above  it  is  compensated  by  the  retarding  ten- 
dency of  the  particles  below  it.  This  molecule,  there- 
fore, ivill  move  as  if  it  were  vibrating  alone,  sup- 
ported by  a  thread  without  weight.  It  fulfills  all  the 
conditions  of  a  simple  pendulum.  This  point  is  called  the 
centre  of  oscillation. 

142.  The  Keal  Length  of  a  Pendulum.— The 

laws  of  the  simple  pendulum  are  applicable  to  the  com- 
pound pendulum  if  we  consider  the  length  of  the  latter  to 
be  the  length  of  the  equivalent  simple  pendulum,  i.  e.,  the 
distance  between  the  centres  of  suspension  and 
oscillation.  We,  therefore,  may  say  that  the  real  length 
of  a  pendulum  is  the  distance  between  the  centre  of  sus- 
pension and  the  centre  of  oscillation.  The  real  length  is 
less  than  the  apparent  length  except  in  the  imaginary  case 
of  the  simple  pendulum. 

143.  First  Law  of  the  Pendulum.— The  vi- 
brations of  a  given  pendulum,  at  any  given  place, 
are   isochronous,  i.  e.y  are  performed  in  equal  times, 
whether  the  arc  be  long  or  short.    Each  pupil   should 
satisfy  himself  of  the  truth  of  this  proposition,  by  the  only 
true  scientific  method,  experiment. 

144.  The    Cycloidal    Pendulum.  —  TJie   law 
above  given  is  strictly  true  only  when   the  pendu- 


THE  PENDULUM. 


FIG.  32. 


lum  vibrates  in  a  cyeloidal   arc.     A  cycloid  is  the 

curve  traced  by  a  point 
in  the  circumference 
of  a  circle  rolling  along 
a  straight  line.  The 
pendulum  may  be 
made  to  move  in  such 
an  arc  by  suspending 
a  small  heavy  ball  by 
a  thread  between  two 
cheeks  upon  which  the 

thread  winds  as  the  pendulum  vibrates.  The  cheeks  must 
be  the  two  halves  of  a  cycloid;  each  cheek  must  have  the 
same  length  as  the  thread.  The  path  of  the  ball  will  be 
a  cycloid,  identical  with  that  to  which  the  cheeks  belong. 

(a.)  The  cyeloidal  pendulum  is  of  little  practical  use.  If  the 
amplitude  of  an  ordinary  pendulum  does  not  exceed  five  degrees, 
the  circular  arc,  thus  described,  will  not  vary  much  from  the  true 
cyeloidal  arc,  and  the  pendulum  will  be  practi- 
cally isochronous.  If  from  the  centre  of  sus- 
pension, with  radius  equal  to  the  length  of  the 
string,  a  circular  arc  be  described,  the  two 
curves  will  sensibly  coincide  for  at  least  five 
degrees.  This  is  why  the  pendulums  of  "reg- 
ulator "  clocks  have  a  small  swing  or  amplitude. 

145.  Second  Law  of  the  Pen- 
dulum.— %e  time  of  vibration  is 
independent  of  the  weight  or  mate- 
rial of  the  pendulum,  depending  only 
upon  the  length  of  the  pendulum,  and 
the  intensity  of  the  force  of  gravity  at 
any  given  place. 

(a.)  Each  pupil  should  try  the  experiment, 
at  home,  with  balls  of  equal  size  but  different  FIG.  33. 


THE  PENDULUM. 


73 


weight.     The  investment  of  a  little  time  and  ingenuity  in  simple 
experiments  will  pay  large  dividends. 

146.  Third  Law  of  the  Pendulum.— The  vibra- 
tions of  pendulums  of  different  lengths  are  performed  in 
different  times.     The  lengths  are  directly  proportional 
to  the  squares  of   the  times  of   vibration,   or    in- 
versely proportional  to  the  squares  of  the  numbers 
of  vibrations  in  a  given  time. 

Note. — Be  careful  to  distinguish  clearly  between  the  expressions 
"times  of  vibration"  and  "numbers  of  vibration."  The  greater 
the  time,  the  less  the  number.  You  may  easily 
verify  by  experiment  the  three  laws  already 
given  for  the  pendulum. 

147.  The  Second's  Pendulum. 

At  the  equator,  the  length  of  a  second's 
pendulum,  at  the  level  of  the  sea,  is 
39  inches ;  near  the  poles,  39.2 ;  in  this 
latitude  about  39.1  inches  or  993.3 
mm.  As  such  a  pendulum  would  be 
inconveniently  long,  use  is  generally  made 
of  one  one-fourth  as  long,  which,  con- 
sequently, vibrates  half  seconds.  The 
length  and  time  of  vibration  of  this 
pendulum  being  thus  known,  the 
length  of  any  other  pendulum  may  be 
found  when  the  time  of  vibration  is 
given ;  or  the  time  of  vibration  may  be 
found  when  the  length  is  given.  The 
third  law  is  applicable  to  such  a  problem. 

148.  Use  of  the  Pendulum  in 
Time-pieces. — The  motion  of  a*  clock  is  due  to  the 
force  of  gravity  acting  upon  the  weights,  or  to  the  elastic- 


FIG.  34. 


74 


THE  PENDULUM. 


ity  of  the  spring.  Bat  the  weights  have  a  tendency  toward 
accelerated  motion  (falling  bodies),  while  the  spring  would 
give  an  example  of  diminishing  motion.  Either  defect 
.would  be  fatal  in  a  time-piece.  Hence  the  properties  of 
the  pendulum  set  forth  in  the  first  and  third  laws  are 
used  to  regulate  this  motion  and  make  it  available  for  the 
desired  end.  If  the  clock  gains  time,  the  pendulum  is 
lengthened  by  lowering  the  bob;  if  it  loses  time,  the  pen- 
dulum is  shortened  by  raising  the  bob. 

149.  Compensation  Pendulums.— The  expan- 
sion of  metals  by  heat  is  a  familiar  fact.  Hence  the  ten- 
Idency  of  a  clock  to  lose  time  in  summer  and 
to  gain  time  in  winter.  One  plan  for  coun- 
teracting this  tendency  is  by  the  use  of  the 
"  gridiron  "  pendulum  which  is  made  of  two 
substances  in  such  a  manner  that  the  down- 
ward expansion  of  one  will  be  exactly  com- 
pensated by  the  upward  expansion  of  the 
other.  In  the  figure,  the  heavy  single  lines 
represent  steel  rods,  the  effect  of  whose  ex- 
pansion will  be  to  lower  the  bob.  The  light 
double  lines  represent  brass  rods,  the  effect  of 
whose  expansion  will  be  to  raise  the  bob.  The 
steel  rod  to*  which  the  bob  is  directly  attached 
passes  easily  through  holes  in  the  two  hori- 
zontal bars  which  carry  the  brass  uprights. 


FIG.  35- 


As  brass  expands  more  than  steel,  for  a  given  increase  of 
temperature,  it  will  be  seen  that  these  two  expansions  may 
be  made  to  neutralize  one  another. 


THE  PENDULUM. 


75 


EXEECISES. 


No. 

INCHES. 

NUMBER. 

TIME. 

No. 

CM. 

NUMBER. 

TIME. 

1 

9 

20  per  min. 

9 

11 

99.33 

? 

? 

2 

? 

30       " 

? 

12 

? 

? 

2  sec. 

3 

30 

? 

? 

13 

? 

? 

2  min. 

4 

16 

? 

? 

14 

24.83 

1 

? 

5" 

? 

? 

|  sec. 

15 

? 

8  per  sec. 

? 

6 

? 

? 

£min. 

16 

397.32 

? 

? 

7 

39.37 

?  per  min. 

i 

17 

11.03 

? 

? 

8 

9 

10      " 

? 

18 

? 

? 

10  sec. 

9 

10 

?  per  sec. 

? 

19 

2483.25 

? 

? 

10 

? 

1  per  min. 

? 

20 

? 

? 

4  sec. 

21.  How  will  the  times  of  vibration  of  two  pendulums  compare, 
their  lengths  being  4  feet  and  49  feet  respectively  ?    Ans.  As  2  to  7. 

22.  Of  two  pendulums,  one  makes  70  vibrations  a  minute,  the 
other  80  vibrations  during  the  same  time  ;    how  do  their  lengths 
compare  ?  Ans.  As  49  to  64. 

23.  If  one  pendulum  is  4  times  as  long  as  another,  what  will  be 
their  relative  times  of  vibration? 

24.  The  length  of  a  second's  pendulum  being  39.1  inches,  what 
must  be  the  length  of  a  pendulum  to  vibrate  in  £  second  ? 

25.  How  long  must  a  pendulum  be  to  vibrate  once  in  8  seconds  ? 
In  $•  second  ? 

26.  How  long  must  a  pendulum  be  to  vibrate  once  in  3^  seconds  ? 

27.  Find  the  length  of  a  pendulum  that  will  vibrate  5  times  in  4 
seconds?  An*.  25.02  +  inches. 

28.  A  pendulum  5  feet  long  makes  400  vibrations  during  a  certain 
time  ;  how  many  vibrations  will  it  make  in  the  same  time  after  the 
pendulum  rod  has  expanded  half  an  inch  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Simple  Pendulum  ;  the  Compound  Pen- 
dulum ;  the  nature  of  the  Motion  of  the  Pendu- 
lum and  its  Cause  ;  the  meaning  of  the  terms  Vi- 
bration, Time  of  Vibration,  Amplitude  of 
Vibration;  Centre  of  Oscillation;  Real  Length 


76  ENERGY. 

of  a  Pendulum ;  Laws  and  Formulas  for  the  Pen- 
dulum ;  the  Cycloidal  Pendulum ;  the  Second's 
Pendulum  ;  the  Use  of  the  Pendulum  in  Clock- 
work; Compensation  Pendulums. 


V. 


ENERGY, 


150.  Work. — This  is  a  world  of  work,  a  world  in 
which  the  necessity  of  working  is  imposed  upon  every 
living  creature.     If  a  man  is  poor,  he  must  work  for  the 
means  of  living;   if  he  is  rich,  still  he  must  work  to  live. 
But  in  physical  science,  the  term  worTc  has  a  broader 
meaning,  and  signifies  the  overcoming  of  resistance 
of  any  kind.     Whether  this  overcoming  of  resistance  is 
pleasant  or  not  does  not  enter  into  consideration  here,  all 
play  being  a  species  of  work.    The  word  is  here  used  in 
this  enlarged,  technical  sense. 

151.  Energy. — Energy    is   the    power   of    doing 
work.    If  one  man  can  do  more  work  than  another,  he 
has  more  energy.     If  a  horse  can  do  more  work,  in  a  given 
time,  than  a  man,  the  horse  has  more  energy  than  the  man. 
If  a  steam-engine  can  do  more  work  than  a  horse,  it  has 
more  energy.    If  a  moving  cannon-ball  can  overcome  a 
greater  resistance  than  a  base-ball  it  has  more  energy. 

152.  Elements  of  Work  Measure.—  Imagine  a 
flight  of  stairs,  each  step  having  a  rise  of  twelve  inches. 
On  the  floor  at  the  foot  of  the  stairs  are  two  weights,  of 


ENERGY.  77 

one  and  ten  pounds  respectively.  Lift  the  first  weight  to 
the  top  of  the  first  step.  How  much  work  have  you  per- 
formed ?  Perhaps  you  will  answer,  one  pound  of  work. 
Now  place  the  second  weight  beside  the  first.  How  much 
work  did  you  perform  in  so  doing  ?  Perhaps  you  will  say 
ten  times  as  much  as  before,  or  ten  pounds.  Now  lift 
each  of  them  another  step,  and  then  another,  until  they 
rest  on  the  top  of  the  tenth  step.  To  lift  the  heavier 
weight  the  second,  third,  and  subsequent  times  involved 
each  as  much  work  as  to  lift  it  the  first  foot,  but  you 
would  hardly  say  that  you  had  lifted  a  hundred  pounds. 
Still  it  is  sure  that  to  place  it  on  the  tenth  step  required 
just  ten  times  as  much  work  as  it  did  to  place  it  on  the  first 
step,  or  just  one  hundred  times  as  much  work  as  it  did  to 
place  the  one  pound  weight  on  the  first  step.  Moreover, 
it  is  evident  that  the  two  elements  of  weight  and 
height  are  necessarily  to  be  considered  in  measuring 
the  work  actually  performed. 

153.  Units   of  Work;    the  Foot-pound.— It 

is  often  necessary  to  represent  work  numerically;  hence 
the  necessity  for  a  unit  of  measurement.  The  unit  com- 
monly in  use,  for  the  present,  in  England  and  this  country 
is  the  foot-pound.  A  foot-pound  is  the  amount  of  work 
required  to  raise  one  pound  one  foot  high  against 
the  force  of  gravity.  The  work  required  to  raise  one  kilo- 
gram one  meter  high  against  the  same  force  is  called  a 
kilogram-meter. 

(a.)  To  get  a  numerical  estimate  of  work,  we  multiply  the  number 
of  weight  units  raised  by  the  number  of  linear  units  in  the  vertical 
height  through  which  the  body  is  raised.  A  weight  of  25  pounds, 
raised  3  feet,  or  one  of  3  pounds  raised  25  feet,  represents  75  foot- 
pounds. A  weight  of  15  Kg.  raised  10  m.,  represents  150  kilogram- 
meters. 


78  ENERGY. 

154.  The   Erg.— The  C.  G.  S.  unit  of  work  is  the 
work   done  by  a  force  of  one   dyne  (§  69)  working 
through  a  distance  of  one    centimeter.    It  is  called 
the  erg;  the  term  is  not  yet  much  used  in  this  country. 

155.  Horse-Power.—^   horse-power   represents 
the   ability  to   perform  33,000  foot-pounds  in  a 
minute.    An  engine  that  can  do  66,000  foot-pounds  in  a 
minute  or  33,000  foot-pounds  in  half  a  minute  is  called  a 
two  horse-power  engine.     To   compute  the    number   of 
horse-powers  represented  by  an  engine  at  work,  multiply 
the  number  of  pounds  raised  by  the  number  of  feet,  and 
divide  the  product  by  33,000  times  the  number  of  minutes 
required  to  do  the  work. 

Note. — Let  the  pupil  make  a  formula  for  horse-power,  similar  to 
those  given  for  falling  bodies. 

156.  Relation  of  Velocity  to  Energy. — Any 

moving  body  can  overcome  resistance,  can  perform  work, 
has  energy.  We  must  acquire  the  ability  to  measure  this 
energy.  In  the  first  place,  we  may  notice  that  the  direc- 
tion of  the  motion  is  unimportant.  A  body  of  given 
weight  and  velocity  can  at  any  instant  do  as  much  work 
when  going  in  one  direction  as  when  going  in  another, 
when  moving  horizontally  as  when  moving  vertically  up- 
ward or  downward.  This  energy  may  be  expended  in 
penetrating  an  earth-bank,  knocking  down  a  wall  or  lifting 
.itself  against  the  force  of  gravity.  Whatever  be  the  work 
actually  done,  it  is  clear  that  the  manner  of  expenditure 
does  not  change  the  amount  of  energy  expended.  We 
may  therefore  find'  to  what  vertical  height  the 
given  velocity  would  lift  the  body,  and  thus  easily 
determine  its  energy  in  foot-pounds,  or  kilogram- 
meters. 


ENERGY.  79 

157.  Ail  Easier  Method.  —  If  we  can  obtain  the 
same  result  without  the  trouble  of  finding  how  high  the 
given  velocity  could  raise  it,  it  is  generally  desirable  to  do 
so.  Be  it  remembered  that  the  two  elements  of  our  meas- 
ure are  units  of  weight  and  units  of  height.  The  first  of 
these  is  given  ;  for  the  second  we  may  substitute  its  equiv- 
alent in  terms  of  the  velocity  which  also  is  given.  The 
determination  of  this  equivalent  is  our  present  problem. 
We  must  use  our  knowledge  of  the  laws  of  falling  bodies. 
Our  vertical  height  is  the  whole  space  passed  over  by  an 
ascending  body  (§  132).  We  have  given  v  to  find  8. 

gt  =  v.        (Formula  1,  Falling  Bodies.) 


9 


S  =  %gP.     (Formula  3,  Falling  Bodies.) 
Substituting  the  above  value  of  f,  we  have, 


Energy  =  ivS  (the  weight  into  the  height).  Substitut- 
ing our  new  value  for  89  we  have  the  following  important 

formula  :  wvz 

Kinetic  Energy  =  -ti  —  . 
0g 

158.  Two  Types  of  Energy.  —  There  are  two  types 
of  energy  which  may  be  designated  as  energy  of  motion 
and  energy  of  position.  With  the  first  of  these  we  are 
familiar.  A  falling  weight  or  running  stream,  possesses 
energy  of  motion  ;  it  is  able  to  overcome  resistance  by 
reason  of  its  weight  and  velocity.  On  the  other  hand,  be- 
fore the  weight  began  to  fall,  while,  as  yet,  it  had  no 


80  ENERGY. 

motion  but  was  at  rest,  it  had  the  power  of  doing  work  by 
reason  of  its  elevated  position  with  reference  to  the  earth. 
When  the  water  of  the  running  stream  was  at  rest  in  the 
lake  among  the  hills  it  had  a  power  of  doing  work,  an 
energy,  which  was  not  possessed  by  the  waters  of  the 
pond  in  the  valley  below.  This  energy  or  power  results 
from  its  peculiar  position.  Energy  of  motion  is  called 
kinetic  energy;  energy  of  position  is  called  potential 
energy. 

159.  Convertibility  of  Kinetic  and  Poten- 
tial Energies. — We  may  at  any  moment  convert  kinetic 
energy  into  potential,  or  potential  energy  into  kinetic. 
One  is  as  real  as  the  other,  and  when  it  exists  at  all,  exists 
at  the  expense  of  a  definite  amount  of  the  other.  Imagine 
a  ball  thrown  upward  with  a  velocity  of  64.32  feet.  As  it 
begins  to  rise  it  has  a  certain  amount  of  kinetic  energy. 
At  the  end  of  one  second  it  has  a  velocity  of  only  32.16  ft* 
Consequently  its  kinetic  energy  has  diminished.  But 
it  has  risen  48.24  ft,  and  has  already  a  considerable  poten- 
tial energy.  All  of  this  potential  energy  results  from  the 
kinetic  energy  which  has  disappeared.  At  the  end  of 
another  second,  the  ball  has  no  velocity;  it  has  reached  the 
turning-point  and  is  at  rest.  Consequently,  it  has  no 
kinetic  energy.  But  the  energy  with  which  it  began  its 
flight  has  not  been  annihilated;  it  has  been  stored  up  in 
the  ball  at  a  height  of  64.32  ft.  as  potential  energy.  If  at 
this  instant  the  ball  be  caught,  all  of  the  energy  may  be 
kept  in  store  as  potential  energy.  If  now  the  ball  be 
dropped,  it  begins  to  lose  its  potential  and  to  gain  kinetic 
energy.  When  it  reaches  the  ground  at  the  end  of  two 
seconds  it  has  no  potential  energy,  but  just  as  much  of  the 


ENERGY. 


81 


kinetic  type  as  was  given  to  it  when  it  began  to  rise.  This 
illustrates  in  a  simple  way  the  important  principle,  the 
transformation  or  convertibility  of  energy  without 
any  change  in  its  quantity. 

160.  Energy   a   Constant    Quantity. — In  the 

case  of  the  ball  thrown  upward,  at  the  start,  at  the  finish, 
or  at  any  intermediate  point  of  either  its  ascent  or  descent, 
the  sum  of  the  two  types  of  energy  is  the  same.  It  may 
be  all  kinetic,  all  potential,  or  partly  both.  In  any  case, 
the  sum  of  the  two  continually  varying  energies  is 
constant.  Just  as  a  man  may  have  a  hundred  gold  dol- 
lars, now  in  his  hand,  now  in  his  pocket,  now  part  in  his 
hand  and  the  rest  in  his  pocket ;  changing  a  dollar  at  a 
time  from  hand  to  pocket  or  vice  versa,  the  amount  of 
money  in  his  possession  remains  constant,  viz.,  one  hun- 
dred dollars. 

161.  Pendulum    Illustration. — The    pendulum 
affords  a  good  and  simple  illustration  of  kinetic  and  poten- 
tial energy,  their  equivalence 

and  convertibility.  When  the 
pendulum  hangs  at  rest  in  a 
vertical  position,  as  P#,  it  has 
no  energy  at  all.  Considered  as 
a  mass  of  matter,  separated  from 
the  earth,  it  certainly  has  po- 
tential energy ;  but  considered 
as  a  pendulum,it  has  no  energy. 
If  the  pendulum  be  drawn 
aside  to  J,  we  raise  it  through 
the  space  ah  ;  that  is,  we  do 
work,  or  spend  kinetic  energy  upon  it.  The  energy  thus 


82  ENERGY. 

expended  is  now  stored  up  as  potential  energy,  ready  to  be 
reconverted  into  energy  of  the  kinetic  type,  whenever  we 
let  it  drop.  As  it  falls  the  distance  lia,  in  passing  from  b 
to  a,  this  reconversion  is  gradually  going  on.  When  the 
pendulum  reaches  a  its  energy  is  all  kinetic,  and  just  equal 
to  that  spent  in  raising  it  from  a  to  b.  This  kinetic  energy 
now  carries  it  on  to  c,  lifting  it  again  through  the  space  ah. 
Its  energy  is  again  all  potential  just  as  it  was  at  b.  If  we 
could  free  the  pendulum  from  the  resistances  of  the  air 
and  friction,  the  energy  originally  imparted  to  it  would 
swing  to  and  fro  between  the  extremes  of  all  potential  and 
all  kinetic;  but  at  every  instant,  or  at  every  point  of  the 
arc  traversed,  the  total  energy  would  be  an  unvarying 
quantity,  always  equal  to  the  energy  originally  exerted  in 
swinging  it  from  a  to  b. 

162.  Indestructibility  of  Energy. — From  the 
last  paragraph  it  will  be  seen  that,  were  it  not  for  friction 
and  the  resistance  of  the  air,  the  pendulum  would  vibrate 
forever ;  that  the  energy  would  be  indestructible.  Energy 
is  withdrawn  from  the  pendulum  to  overcome  these  imped- 
iments, but  the  energy  thus  withdrawn  is  not  destroyed. 
What  becomes  of  it  will  be  seen  when  we  come  to  study 
heat  and  other  forms  of  energy,  which  result  from  the 
motions  and  positions  of  the  molecules  of  matter.  The 
truth  is  that  energy  is  as  indestructible  as  matter. 
For  the  present  we  must  admit  that  a  given  amount  of 
energy  may  disappear,  and  escape  our  search,  but  it  is  only 
for  the  present.  We  shall  soon  learn  to  recognize  the 
fugitive  even  in  disguise. 

Note. — Physics  may  now  be  defined  as  the  science  of  matter  and 
energy. 


ENERGY. 


EXEKCISES. 

1.  How  many  horse-powers  in  an  engine  that  will  raise  8,250  Ibs. 
176  ft.  in  4  minutes  ? 

2.  A  ball  weighing  192.96  pounds  is  rolled  with  a  velocity  of  100 
feet  a  second.    How  much  energy  has  it  ?    Ans.  30000  foot-pounds. 

3.  A  projectile  weighing  50  Kg.  is  thrown  obliquely  upward  with 
a  velocity  of  19.6  in.     How  much  kinetic  energy  has  it  ? 

4.  A  ten-pound  weight  is  thrown  directly  upward  with  a  velocity 
of  225.12  ft.    (a.)  What  will  be  its  kinetic  energy  at  the  end  of  the 
third  second  of  its  ascent?    (&.)  At  the  end  of  the  fourth  second  of 
its  descent  ? 

5.  A  body  weighing  40  Kg.  moves  at  the  rate  of  30  Km.  per  hour. 
Find  its  kinetic  energy. 

6.  What  is  the  horse -power  of  an  engine  that  can  raise  1,500 
pounds  2,376  feet  in  3  minutes? 

7.  A  cubic  foot  of  water  weighs  about  62|  pounds.    What  is  the 
horse-power  of  an  engine  that  can  raise  300  cubic  feet  of  water 
every  minute  from  a  mine  132  ft.  deep  ? 

8.  A  body  weighing  100  pounds  moves  with  a  velocity  of  20  miles 
per  hour.     Find  its  kinetic-  energy. 

9.  A  weight  of  3  tons  is  lifted  50  feet.    (#.)  How  much  work  was 
done  by  the  agent?    (6.)  If  the  work  was  done  in  a  half -minute, 
what  was  the  necessary  horse-power  of  the  agent? 

10.  How  long  will  it  take  a  two  horse-power  engine  to  raise  5 
tons  100  feet  ? 

11.  How  far  can  a  two  horse-power  engine  raise  5  tons  in  30  sec.  ? 

12.  What  is  the  horse-power  of  an  engine  that  can  do  1,650,000 
foot-pounds  of  work  in  a  minute  ? 

13.  What  is  the  horse-power  of  an  engine  that  can  raise  2,376 
pounds  1,000  feet  in  2  minutes  ? 

14.  If  a  perfect  sphere  rest  on  a  perfect,  horizontal  plane  in  a 
vacuum,  there  will  be  no  resistance  to  a  force  tending  to  move  it. 
How  much  work  is  necessary  to  give  to  such  a  sphere,  under  such 
circumstances,  a  velocity  of  20  feet  a  second,  if  the  sphere  weighs 
201  pounds  ? 

15.  A   railway  car  weighs  10  tons.     From  a  state  of  rest  it  is 
moved  50  feet,  when  it  is  moving  at  the  rate  of  3  miles  an  hour. 
If  the  resistances  from  friction,  etc.,  are  8  pounds  per  ton,  how 
many  foot-pounds  of  work  have  been  expended  upon  the  car? 
(First  find  the  work  done  in  overcoming  friction,  etc.,  through  50  ft. 
which  is  50  foot-pounds  x  10  x  8.     To  this  add  the  work  done  in 
giving  the  car  kinetic  energy.) 


84  ENERGY. 

Recapitulation. — In  this  section  we  have  considered 
the  meaning  of  \Vork  and  Energy ;  the  Ele- 
ments of  Work-measure;  the  Unit  of  Work,  as 
Foot-pound  or  K.ilogram-meter ;  Horse- 
power; the  relation  between  Velocity  and  En- 
ergy ;  a  very  convenient  Formula  for  Energy ; 
two  Types  of  Energy,  Kinetic  and  Potential ; 
the  mutual  Convertibility  of  these  two  Types  of 
Energy ;  the  Sum  of  these  two  as  a  Constant  Quan- 
tity ;  the  Pendulum  as  an  Illustration  of  this  Con- 
vertibility and  Constancy;  the  Indestructibility  of 
Energy. 

REVIEW  QUESTIONS  AND  EXEECISES. 

1.  (a.)  What  is  a  molecule  ?    (6.)  An  atom?    (c.)  Name  the  attrao 
tions  pertaining  to  each. 

2.  (a.)  Give  an  original  illustration  of  a  physical  change,    (ft.)  Of 
a  chemical  change. 

3.  (a. )  What  is  the  difference  between  general  and  characteristic 
properties  of  matter?    (&.)  Give  an  illustration  of  impenetrability, 
not  mentioned  in  the  book. 

4.  (a.)  Upon  what  property  do  most  of  the  characteristic  proper- 
ties of  matter  depend  ?    (6.)  Name  five  general  and  three  charac- 
teristic properties  of  matter,    (c.)  Define  inertia. 

5.  (a.)  How  does  a  solid  differ  from  a  liquid  ?    (&.)  From  a  gas  ? 
(c.)  How  does  a  gas  differ  from  a  vapor  ?    (d.)  What  is  a  fluid  ? 

6.  (a.)  Define  dynamics.      (&.)  What  is  the  difference  between 
statics  and  kinetics  ?    (c.)  What  is  the  gravity  unit  of  force  ?    (d.) 
The  kinetic  unit  ? 

7.  («.)  Give  Newton's  Laws  of  Motion.     (&.)  Explain  the  meaning 
of  "parallelogram  of  forces."    (c.)  What  is  an  equilibrant  ?    (d.) 
Give  the  law  of  reflected  motion. 

8.  (a.)  What  is  the  difference  between  gravity  and  gravitation? 
(&.)  Give  the  law  of   gravitation,     (e.)  Of  weight,    (d.)  What  is 
meant  by  centre  of  gravity  ? 

9.  (a.)  Describe  the  several  kinds  of    equilibrium.     (6.)  Upon 
what  does  the  stability  of  a  body  depend?    (c.)  Show  how.     (d.) 
What  is  the  line  of  direction  ? 


ENERGY.  85 

10.  («.)  Why  is  it  that  a  lead  ball  and  a  wooden  ball  will  fall  100 
feet  in  the  same  time?    (&.)  How  did  Galileo  study  the  laws  of 
falling  bodies?    (c.)  Who  was  Galileo  and  when  did  he  live?    (d.) 
Define  increment  of  velocity. 

11.  (a.)  Give  the  laws  of  freely  falling  bodies.     (&.)  Express  the 
same  truths  algebraically,    (c.)  What  forces  act  upon  a  projectile  ? 
(d.)  Define  random. 

12.  (a.)  What  is  a  simple  pendulum?     (&.)  A  compound  pen- 
dulum?   (e.)  What  is  the  real  length  of  a  pendulum?    (d.)  How 
long  must  a  pendulum  be  to  vibrate  once  a  minute  ?    (e.)  Once  a 
second  ?    (/. )  What  is  the  most  important  property  of  a  pendulum  ? 

13.  Two  forces  of  6  and  8  pounds  respectively  act  at  right  angles 
to  each  other.    Find  the  direction  and  intensity  of  their  equilibrant. 

14.  («.)  Define  energy.     (&.)  Foot-pound,    (c.)  Horse-power,    (d.) 
Give  the  rule  for  calculating  horse-power. 

15.  («.)  What  is  a  kilogram-meter?     (&.)  Give  the  formula  for 
the  calculation  of  kinetic  energy  from  weight  and  velocity,     (c.) 
Deduce  the  same. 

16.  (a.)  State  fully  and  clearly  the  difference  between  kinetic  and 
potential  energy.     (&.)  Illustrate  the  same  by  the  pendulum. 

17.  (a.)  What  is  the  object  of  experiments  in  the  study  of  phy- 
sics?   (6.)  What  is  the  metric  unit  of  weight?    (c.)  How  is  it  ob- 
tained ? 

18.  Three  inelastic  balls  weighing  5,  7  and  8  pounds,  lie  in  the 
same  straight  line.     The  first  strikes  the  second  with  a  velocity  of 
60  feet  per  second  ;  the  first  and  second  together  strike  the  third. 
What  will  be  the  velocity  of  the  third  ? 


SIMPLE    MACHINES. 


i. 


PRINCIPLES    OF    MACHINERY.—  THE    LEVER. 

163.  What  is  a  Machine?—^  machine  is  a 
contrivance  by  means  of  which  the  power  can  be 
applied  to  the  resistance  more  advantageously.    Its 
general  office  is  to  effect  a  transformation  in  the  inten- 
sities of  energies,  so  that  an  energy  of  small  intensity, 
acting  through  a  considerable  distance,  may  be  made  to 
reappear  as  an  energy  of  considerable  intensity,  acting 
through  a  small  distance,  or  vice  versa. 

164.  A   Machine  cannot  Create   Energy.  — 

No  machine  can  create  or  increase  energy.  In  fact,  the 
use  of  a  machine  is  accompanied  by  a  waste  of  power 
which  is  needed  to  overcome  the  resistances  of  friction,  the 
air,  etc.  A  part  of  the  energy  exerted  must  therefore  be 
used  upon  the  machine  itself,  thus  diminishing  the  amount 
that  can  be  transmitted  or  utilized  for  doing  the  work  in 
hand. 

165.—  A  Common  Error.  —  A  clear  understanding 
of  this  fact  is  very  important.    Tfiere  is  a  very  common 


PRINCIPLES   OF  MACHINERY.  87 

erroneous  notion  that,  in  some  way  or  other,  a 
machine  performs  worlc  of  itself — that  it  is  a  source  of 
power.  It  were  as  reasonable  to  imagine  that  a  bank  is  a 
source  of  real  money.  The  bank  can  pay  out  no  more 
than  it  receives ;  neither  can  a  machine.  A  man  may  go 
to  the  bank  with  a  ten-dollar  gold  piece,  and  get  for 
it  ten  one-dollar  gold  pieces.  In  like  manner,  he  may  go 
to  a  machine  with  an  ability  of  moving  ten  pounds  one 
foot  in  a  given  time,  and  get  for  it  the  ability  of  moving 
one  pound  ten  feet  in  the  same  time.  He  may  exchange 
what  he  has  for  what  he  prefers ;  but,  in  the  case  of  the 
bank  and  of  the  machine  alike,  the  equivalent  must  be 
paid,  and  generally  a  commission  for  the  transfer. 

166.  Of  what  Use  are  Machines?— Some  of  the 
many  advantages  resulting  from  the  use  of  machines  are : 
(1.)  It  enables  us  to  exchange  intensity  for  a  velocity 

otherwise  unattainable,  as  in  the  case  of  the  sewing 
machine  or  spinning  wheel. 

(2.)  It  enables  us  to  exchange  velocity  for  an  intensity  of 
power  otherwise  unattainable,  as  in  the  case  of  lift- 
ing a  large  stone  with  a  crow-bar  or  pulleys. 

(3.)  It  enables  us  to  change  the  direction  of  our  force,  as 
in  the  case  of  hoisting  a  flag  on  a  flag-staff.  It 
would  be  inconvenient  to  climb  the  pole  and  then 
draw  up  the  flag. 

(4.)  It  enables  us  to  employ  other  forces  than  our  own,  as 
the  strength  of  animals,  the  forces  of  wind,  water, 
steam,  etc. 

167.  General  Laws  of  Machines.— The  work  to 
be  done  by  a  machine  is  generally  called  the  weight  or 
load.     The  work  of  the  power  (e.g.,  foot-pounds)  is  always 


88  THE  LEVER. 

equal  to  the  work  of  the  load,  the  power  expended  in  the 
machine  itself  being  disregarded.  The  following  laws  are, 
therefore,  applicable  to  machines  of  every  kind.  They  are 
called  the  general  or  great  laws  of  machines : 

(I.)  What  is  gained  in  intensity  of  power  is  lost 
in  time,  velocity,  or  distance;  and  what  is 
gained  in  time,  velocity,  or  distance  is  lost  in  inten- 
sity of  power. 

(2.)  Tlie  power  multiplied  by  the  distance  through 
which  it  moves,  equals  the  iveight  multiplied 
by  the  distance  through  which  it  moves. 

(3.)  The  power  multiplied  by  its  velocity,  equals  the 
weight  multiplied  by  its  velocity. 

168.  What  is  a  Lever? — A  lever  is  an  inflex- 
ible   bar  capable  of  being   freely    moved    about  a 
fixed  point  or  line,  called  the  fulcrum. 

In  every  lever,  three  points  are  to  be  considered,  viz.-, 
the  fulcrum  and  the  points  of  application  for  the  power 
and  the  weight.  Every  lever  is  said  to  have  two  arms. 
The  power-arm  is  the  perpendicular  distance  from  the  ful- 
crum to  the  line  in  which  the  power  acts ;  the  weight-arm 
is  the  perpendicular  distance  from  the  fulcrum  to  the  line 
in  which  the  weight  acts.  If  the  arms  are  not  in  the  same 
straight  line,  the  lever  is  called  a  bent  lever. 

169.  Classes  of  Levers* — There  are  three  classes 

of  levers,  depending  upon  the 
relative  positions  of  the  power, 
weight,  and  fulcrum. 

FIG.  37.  (1.)  If  the  fulcrum   is  be- 


THE  LEVER. 


89 


FIG.  38. 


tween  the  power  and  weight  (P.  F.  W. ),  the  lever  is  of 
the  first  class  (Fig.  37);  e,  g.,  crowbar,  balance,  steelyard, 
scissors,  pincers. 

(2.)  If  the  weight  is  be- 
tween the  power  and  the 
fulcrum  (P.  W.  F.),  the 
lever  is  of  the  second  class 
(Fig.  38) ;  e.  #.,  cork-squeezer, 
nut-cracker,  wheel-barrow. 

(3.)  If  the  power  is  be- 
tween the  weight  and  the  ful- 
crum (W.  P.  F.),  the  lever  is  ^ 
of  the  third  class  (Fig.  39); 
e.  g.,  fire- tongs,  sheep-shears, 
human  fore-arm.  FlG-  39- 

17O.  Static  Laws  of  the  Lever.— It  will  be 
clearly  seen  or  may  be  geometrically  shown  that  the  ratio 
between  the  arms  of  the  lever  will  be  the  same  as  the  ratio 
between  the  velocities  of  the  power  and  the  weight,  and 
the  same  as  the  ratio  between  the  distances  moved  by  the 
power  and  the  weight.  If  the  power-arm  be  twice  as  long 
as  the  weight-arm,  the  power  will  move  twice  as  fast  and 
twice  as  far  as  the  weight  does.  The  general  laws  of  ma- 
chines may  therefore  be  adapted  to  the  lever  as  follows  : 

P  x  power-arm  =W  x  weight-arm,  or  P  x  PF  =W  xWF. 


/.  P  :  W  :: 

(1.)  In  the  case  of  the  lever,  the  power  and  weight  are 
inversely  proportional  to  the  corresponding  arms  of  the 
lever;  or, 


90  THE    LEVER. 

(2.)  The  power  multiplied  by  the  power-arm  equals  the 
weight  multiplied  by  the  weight-arm  ;  or, 
•A  (3.)  A  given  power  ivill  suppoH  a  weight  as  many 
times  as  great  as  itself,  as  the  power-arm  is  times  as 
long  as  the  weight-arm. 

Note. — A  static  law  expresses  the  relation  between  the  power  and 
weight  when  the  machine  is  in  equilibrium.  In  order  that  there  be 
motion,  one  of  the  products  mentioned  in  the  law  above  must  be 
greater  than  the  other.  The  lever  itself  must  be  in  equilibrium 
before  the  power  and  weight  are  applied.  It  is  to  Be  noticed  that 
when  we  speak  of  the  power  multiplied  by  the  power-arm,  we  refer 
to  the  abstract  numbers  representing  the  power  and  power-arm. 
We  cannot  multiply  pounds  by  feet,  but  we  can  multiply  the  number 
of  pounds  by  the  number  of  feet. 

171.  The  Moment   of  a  Force.— The  moment 
of  a  force  acting  about  a  given  point,  as  the  fulcrum  of  a 
lever,  is  the  product  of  the  numbers  representing 
respectively   the  magnitude  of  the  force  and  the 
perpendicular    distance    between    the  given    point 
and   the    line    of  the   force.      In   the    case    of    the 
lever  represented   in    Fig.  37,  the  weight-arm  is  8  mm. 
and  the  power-arm  is  30  mm.    Suppose  that  the  power  is 
4  grams,  and  let  the  weight  be  represented  by  x.     Then 
the  moment  of  the  force  acting  on  the  power-arm  will  be 
represented  by  (4  x  30  =)  120,  and  the  moment  of  the 
force  acting  on  the  weight-arm  by  82. 

172.  Moments  Applied  to  the  Lever. — We 

sometimes  have  sey- 
1H 

eral  forces    acting 

, 10 I 30  upon  one  or  both 

c|  J  e\  /      arms  of  a  lever,  in 

1 1  • 

or    in 


i  8  2  i 

FIG.  40.  opposite  directions. 


THE  LEVER, 


91 


Under  such  circumstances,  the  lever  will  be  in  equilibrium, 
when  the  sum  of  the  moments  of  the  forces  tending  to 
turn  the  lever  in  one  direction  is  equal  to  the  sum  of  the 
moments  of  the  forces  tending  to  turn  the  lever  in  the 
other  direction.  Eepresenting  the  moments  of  the  several 
forces  acting  upon  the  lever  represented  in  the  figure  by 
their  respective  letters  and  numerical  values,  * 

b  +  c  +  d  =  a  +  e  +  f        30  +  30  +  40  =  30  +  25  +  45. 
or,  c  +  d—  a  =  e  +  f—l         30  +  40—30  =  25  +  45—30. 

173.  Bent  Levers.  —  When  the  lever  is  not  a 
straight  bar,  or  ivhen,  for  any  reason,  the  power  and 
weight  do  not  act  parallel  to  each 
other,  it  becomes  necessary  to  distinguish 
between  the  real  and  apparent  arms  of  the 
lever.  This  will  be  easily  done,  if  you  are 
familiar  with  the  definition  of  the  arms 
of  a  lever,  given  in  §  168.  In  Fig.  41,  we 
have  represented  a  very  simple  kind  of 
bent  lever,  which  is  sufficiently  explained 
by  the  engraving.  In  Fig.  42,  we  have  a 
representation  of  a  curved  rod  lever,  W'P',  at  the  ends  of 

which  two  forces, 
/\  not  parallel,   are 

"W"  ''          v*v» 

/\        /  \^  acting.     Our  def- 

Xlr//  inition     of     the 

arms  of  the  lever, 
already  learned, 
removes  every  dif 
ficulty  arising  from  the  form  of  the  lever,  or  the  direction 
in  which  the  forces  act.  The  arms  are  not  FP'  and  FW', 
but  FP  and  FW. 


FIG.  41. 


FIG.  42. 


92  THE  LEVER. 

174.   Load    between   Two    Supports.—//  a 

beam  rest  on  two  supports,  and  carry  a  load  be- 
tween them,  the  beam  may  be  considered  a  lever 
of  the  second  class.  The  part  carried  by  either  support 
may  be  found  by  considering  it  as  the  power,,  and  the 
other  support  as  the  fulcrum.  (Fig.  43.) 


FIG.  43. 


175.  The  Balance. — The  balance  is  essentially 
a  lever  of  the  first  class,  having  equal  arms.  Its 
use  is  to  determine  the  relative  weights  of  bodies.  Its 
action  depends  upon  the  equality  of  moments  explained  in 
§  171  and  §  172.  The  lever  itself  is  called  the  beam. 
From  the  ends  of  the  beam  are  suspended  two  pans,  one 
to  carry  the  weights  used,  the  other  to  carry  the  article  to 
be  weighed.  An  index  needle,  or  pointer,  is  often  attached 
to  the  beam,  and  indicates  equilibrium,  by  pointing  to  the 
zero  of  a  graduated  scale,  carried  by  a  fixed  support. 

(a.)  That  the  balance  may  be  accurate,  the  arms  must  be  of  the  same 
length.  To  make  these  arms  exactly  equal  is  far  from  an  easy  task. 
That  the  balance  may  be  delicate,  it  must  turn  upon  its  axis  with 


THE  LEVER. 


93 


little  friction,  the  axis  of  support  must  be  a  very  little  above  the 
centre  of  gravity,  the  arms  must  be  of  considerable  length,  and  the 
beam  must  be 
light.  Balances  are 
made  so  delicate 
that  they  may  be 
turned  by  less  than 
a  thousandth  of  a 
grain.  The  sup- 
porting edge  of  the 
axis  is  made  very 
sharp  and  hard, 
and  rests  upon  two 
supports,  general- 
ly made  of  agate 
or  polished  steel. 
A  really  good  bal- 
ance is  an  expen- 
sive piece  of  appa- 
ratus. 


FIG.  44. 


176.  False  Balances. — False  balances  (levers  of 
the  first  kind  with  unequal  arms)  are  sometimes 
used  by  dishonest  dealers.    When  buying,  they  place 
the  goods  on  the  shorter  arm ;  when  selling,  on  the  longer. 
The  cheat  may  be  exposed  by  changing  the  goods  and 
weights  to  the  opposite  sides  of  the  balance.     The  true 
weight  may  be  found  by  weighing  the  article  first  on  one 
side  and  then  on  the  other,  and  taking  the  geometrical 
mean  of  the  two  false  weights ;   that  is,  by  finding  the 
square-root  of  the  product  of  the  two  false  weights. 

177.  Double  Weighing. — In  another  way  the  true 
weight  of  a  body  may  be  found  with  a  false  balance.     The 
article  to  be  weighed  is  placed  in  one  pan,  and  a  counter- 
weight, as  of  shot  or  sand,  placed  in  the  other  pan  until 
equilibrium  is  produced.    The  article  is  then  removed, 
and  known  weights  placed  in  the  pan  until  equilibrium  is 


94 


THE  LEVER. 


again  produced.     The  sum  of  these  weights  will  be  the 
true  weight  of  the  given  article. 

178.  Compound  Lever.—  Sometimes  it  is  not  con- 
venient to  use  a  lever  sufficiently  long  to  make  a  given 
power  support  a  given  weight.  A  combination  of  levers 
called  a  compound  lever  may  then  be  used.  Hay-scales 
may  be  mentioned  as  a  familiar  illustration  of  the  com- 
pound lever.  In  this  case  we  have  the  following : 

Statical  Law.— Tl%e  contin- 
ued product  of  the  power  and 
tJie  lengths  of  the  alternate 
arms,  beginning  with  the 
power-arm,  equals  the  contin- 
ued product  of  the  weight 
and  the  lengths  of  the  alter- 
nate arms  beginning  ivith  the 
weight-arm. 


FIG.  45. 


EXERCISES. 


No. 
1 

1^ 

Id 

Power. 

I 

i 

No. 
IT 

1* 

Us 

1 

+j 

§ 

i 

Lever. 

& 

£* 

Length. 

Class. 

4ft. 

2ft. 

501bs. 

? 

5ft. 

•? 

50  Ibs. 

25  Ibs. 

10ft. 

? 

2 

3ft. 

9ft. 

? 

751bs. 

12 

? 

9 

15  oz. 

45  oz. 

12  in. 

2 

3 

10ft. 

4ft. 

141bs. 

? 

13 

? 

50cm. 

iKg. 

4  Kg. 

? 

2 

4 

60  in. 

I 

21bs. 

30  Ibs. 

14 

163  cm. 

? 

12  oz. 

2oz. 

y 

3 

5 

? 

18cm. 

27  Kg. 

9  Kg. 

15 

3ft. 

5ft. 

10  Ibs. 

? 

? 

1 

6 

14ft. 

10 

45  oz. 

63  oz. 

16 

39.37  in. 

50cm. 

? 

20  Kg. 

? 

1 

7 

40cm. 

56cm. 

21  g. 

? 

.17 

? 

16ft. 

14  Ibs. 

3*  Ibs. 

16ft. 

? 

8 

18  in. 

21  in. 

? 

24  oz. 

18 

'? 

2ft. 

30  Ibs. 

? 

10ft. 

1 

9 

26cm. 

y 

11  Dg. 

13  Dg. 

19 

? 

2ft. 

30  Ibs. 

? 

10ft. 

2 

10 

? 

1ft. 

501bs. 

2500  Ibs. 

20 

2ft. 

? 

30  Ibs. 

? 

10ft. 

3 

Note  to  the  Pupil. — If  any  of  these  problems  be  obscure  to  you. 
remember  that  it  will  pay  to  draw  an  accurate  figure  or  diagram  of 
the  machine  representing  the  several  powers  and  weights  in  position. 
Bee  Fig.  40. 


THE  LEVER.  95 

21.  If  a  power  of  50  pounds  acting  upon  any  kind  of  machine, 
move  15  feet,  (a)  how  far  can  it  move  a  weight  of  250  pounds  ? 
(&.)  How  great  a  load  can  it  move  75  feet  ? 

22.  If  a  power  of  100  pounds  acting  upon  a  machine,  moves  with 
a  velocity  of  10  feet  per  second,  (a)  to  how  great  a  load  can  it 
give  a  velocity  125  feet  per  second  ?    (&.)  With  what  velocity  can  it 
move  a  load  of  200  pounds  ? 

23.  A  lever  is  10  feet  long  ;   F  in  the  middle ;   a  power  of  50 
pounds  is  applied  at  one  end  ;   (a)  how  great  a  load  at  the  other  end 
can  it  support  ?    (6.)  How  great  a  load  can  it  lift  ? 

Ans.  to  (&.)  :  Anything  less  than  50  Ibs. 

24.  The  power-arm  of  a  lever  is  10  feet ;  the  weight-arm  is  5  feet. 
(a.)  How  long  will  the  lever  be  if  it  is  of  the  first  class  ?    (&.)  If  it 
is  of  the  second?     (c.)  If  it  is  of  the  third  class? 

25.  A  bar  12  feet  long  is  to  be  used  as  a  lever,  keeping  the  weight 
3  feet  from  the  fulcrum,     (a.)  What  class  or  classes  of  levers  may 
it  represent  ?    (&.)  What  weight  can  a  power  of  10  pounds  support 
in  each  case  ? 

26.  Length  of  lever  =  10  feet.    Four  feet  from  the  fulcrum  and  at 
the  end  of  that  arm  is  a  weight  of  40  pounds  ;  two  feet  from  the 
fulcrum  on  the  same  side,  is  a  weight  of  1,000  pounds.    What  force 
at  the  other  end  will  counterbalance  both  weights  ? 

27.  At  the  opposite  ends  of  a  lever  20  feet  long,  two  forces  are 
acting  whose  sum  =  1,200  pounds.     The  lengths  of  the  lever  arms 
are  as  2  to  3  ;  what  are  the  two  forces  when  the  lever  is  in  equi- 
librium ? 

28.  Length  of  lever  =  8  feet,  F  in  the  centre.      A  force  of  10 
pounds  acts  at  one  end,  one  foot  from  it  another  of  100  pounds. 
Three  feet  from  the  other  end  is  a  force  of  100  pounds.     Direction 
of  all  forces,  downward.     Where  must  a  downward  force  of  80 
pounds  be  applied  to  balance  the  lever  ? 

29.  Length  of  lever  db  =  6^  feet ;  fulcrum  at  c ;  a  downward 
force  of  60  pounds  acts  at  a  ;  one  of  75  pounds  at  a  point  d  between 
a  and  c,  2|  feet  from  the  fulcrum  ;  required  the  amount  of  equili- 
brating force  acting  at  &,  the  distance  between  &  and  c  being  £  feet. 

30.  On  a  lever  db,  a  downward  force  of  40  pounds  acts  at  a,  10 
feet  from  fulcrum  c;  on  same  side  and  6^  feet  from  c,  an  upward 
force,  d,  acts,  amounting  to  56  pounds ;   distance  be  =  3  feet  :    a 
downward  force  of  96  pounds  acts  at  &.    (a.)  Where  must  a  fourth 
force  of  28  pounds  be  applied  to  balance  the  lever,  and  (&)  what 
direction  must  it  have  ? 

31.  A  beam  18  feet  long  is  supported  at  both  ends  ;  a  weight 
of  1  ton  is  suspended  3  feet  from  one  end,  and  a  weight  of  14  cwt.. 


96  THE  LEVER. 

8  feet  from  the  other  end.     Give  the  pressure  on  each  point  of  sup- 
port. 

32.  Length  of  lever  =  3  feet ;  where  must  the  fulcrum  be  placed 
so  that  a  weight  of  200  Ibs.  at  one  end  shall  be  balanced  by  40  Ibs. 
at  the  other  end  ? 

33.  In  one  pan  of  a  false  balance,  a  roll  of  butter  weighs  1  Ib. 

9  oz. ;  in  the  other,  2  Ibs.  4  oz.    Find  the  true  weight. 

34.  A  and  B  at  opposite  ends  of  a  bar  6  ft.  long  carry  a  weight 
of  300  Ibs.  suspended  between  them.     A's  strength  being  twice  as 
great  as  B's,  where  should  the  weight  be  hung  ? 

35.  A  and  B  carry  a  quarter  of  beef  weighing  450  pounds  on  a 
rod  between  them.     A's  strength  is  1}  that  of  B's;  the  rod  is  8 
feet  long  ;  where  should  the  beef  be  suspended  ? 

36.  Length  of  lever  =  16  feet ;  weight  at  one  end,  100  pounds  : 
what  power  applied  at  other  end,  3£-  feet  from  the  fulcrum,  is  re- 
quired to  move  the  weight  ? 

37.  A  power  of  50  Ibs.  acts  upon  the  long  arm  of  a  lever  of  the 

first  class  ;  the  arms  of  this  lever  are  5  and  40  inches  respectively. 
The  other  end  acts  upon  the  long  arm  of  a  lever  of  the  second 
class  ;  the  arms  of  this  lever  are  6  and  33  inches  respectively,  (a.) 
Figure  the  machine.  (6.)  Find  the  weight  that  may  be  thus  sup- 
ported, (c.)  What  power  will  support  a  weight  of  4,400  kilograms? 

Recapitulation. — To  be  amplified  by  the  pupil  for 
review. 

f  DEFINITION. 
RELATION  TO  ENERGY. 
USE. 
GENERAL  LAWS. 


THE  LEVER. 


BENT. 
COMPOUND. 

MOMENTS  OF  FORCES. 


DEFINITION. 
ARMS. 

STATIC  LAWS. 

(  True. 


CLASSES. 


1.  BALANCE.-! 

False.  , 

i  Weighing. 

2.  LOAD    BETWEEN  TWO  SUPPORTS. 


THE    WHEEL    AND    AXLE. 


ECTfON  II. 


THE   WHEEL  AND   AXLE   AND   WHEEL-WORK. 

179.  The  Wheel  and  Axle.— The  wheel  and 
axle  consists  of  a  wheel  united  to  a  cylinder  in 
such  a  way  that  they  may  revolve  together  about 
a  common  axis.  It  is  a  modified  lever  of  the  first 
class. 

ISO.  Advantages  of  the  Wheel  and  Axle.— 

The  ordinary  range  of  action  of  a  lever  of  the  first  class 

is  very  small.    In  order  to  raise  the 

load  higher  than  the  vertical  distance 

through  which  the  weight  end  of  the 

lever  passes,  it  is  necessary  to  support 

the  load  and  re-adjust  the  fulcrum. 

This  occasions  an  internlittent  action 

and  loss  of  time,  difficulties  which  are 

obviated  by  using  the  wheel  and  axle. 


FIG.  46. 


181.  A  Modified  Lever. — Considered  as  a  lever 
of  the  first  class,  the  fulcrum  is  at 
the  common  axis,  while  the  arms  of 
the  lever  are  the  radii  of  the  wheel 
and  of  the  axle.  If  a  c,  the  radius 
of  the  wheel,  be  used  as  the  power- 
arm,  velocity  or  time  is  exchanged 
for  intensity  of  power.  This  is  the 
usual  arrangement.  If  be,  the  radius 
FIG.  47.  of  the  axle,  be  used  as  the  power- 


98  THE    WHEEL  AND  AXLE. 

arm,  there  will  be  an  exchange  of  intensity  of  power  for 
velocity  or  time.  In  treating  of  the  wheel  and  axle,  unless 
otherwise  specified,  reference  is  made  to  the  former  or  usual 
arrangement. 

182.   Formulas  for  Wheel  and  Axle.—  The 
law  and  formula  for  the  lever  apply  here  : 

P  :   W  :  :   WF  :  PF,        or,     P  :  W  :  :  r  :  R, 


the  radii  of  the  wheel  and  of  the  axle  respectively  being 
represented  by  R  and  r.  But  it  is  a  geometrical  truth 
that  in  any  two  circles,  the  ratio  of  their  radii  is  the  same 
as  the  ratio  of  their  diameters  or  circumferences.  Hence 
=n  these  ratios  may  be  substituted  for 

n      „__,       r-r    the  ratio  between  the  radii  of  the 

cJy  u   mm.       L  =, 

wheel  and  axle;  or, 

P  :   W  :  :   r  :  R. 
P  :   W  :  :  cl  :  D. 


FIG.  48.  P  :   W  ::   c  :  C. 

183.  Law  of  Wheel  and  Axle.  —  TJie  power 
multiplied    by    the    radius,    diameter   or    circum- 
ference of  the  wheel  equals  the  weight  multiplied 
by  the  corresponding  dimension  of  the  axle. 

Note.  —  If  the  radius  of  the  axle  be  made  the  powver-arm,  the  for- 
mulas will  be  as  follows  : 

P  :  W  :  :   WF  :  PF,        or,    P  :  W  :  :  D  :  d  . 

184.  Various  Forms  of  Wheel  and  Axle.  — 

The  wheel  and  axle  appears  in  various  forms.  It  is  not 
necessary  that  an  entire  wheel  be  present,  a  single  spoke 
or  radius  being  sufficient  for  the  application  of  the  power, 


THE    WHEEL   AND  AXLE. 


99 


FIG.  49. 


as  in  the  case  of  the  windlass  (Fig.  48)  or  capstan  (Fig.  49). 

In  all  such  cases,  the  radius  being 

given,  the  diameter  or  circumference 

of  the  wheel  may  be  easily  computed. 

In  one  of  the  most  common  forms, 

the  power  is  applied  by  means  of  a 

rope  wound  around  the  circumference 

of  the  wheel.      When  this  rope  is 

unwound  by  the  action  of  the  power,  another  rope  is  wound 

up  by  the  axle,. and  the  weight  thus  raised. 

185.  Wheel- work.— Another  method  of  securing 

a  great  difference  in  the  in- 
tensities of  balancing  forces, 
is  to  use  a  combination  of 
wheels  and  axles  of  moder- 
ate size.  Such  a  combination 
constitutes  a  train.  The  wheel 
that  imparts  the  motion  is 
called  the  driver  ;  that  which 
receives  it,  the  follower.  An 
axle  with  teeth  upon  it  is 
called  a  pinion.  The  teeth  or 
cogs  of  a  pinion  are  called  leaves. 

186.  Law  of  Wheel-work.— A  train  of  wheel- 
work  is  clearly  analogous  to  a  compound  lever ;  the  statical 
law,  given  in  §  178,  may  be  adapted  to  our  present  pur- 
poses as  follows :     TJie  continued  product  of  the  power 
and  the  radii  of  the  ivheels  equals  the  continued 
product  of  the  weight  and  the  radii  of  the  axles. 

187.  Another     Law    of    Wheel-work.— By 

examination  of  Fig.  50,  it  will  be  seen  that  while  the  axle 


FIG.  50. 


100  WHEEL-WORK. 

d  revolves  once,  the  wheel  and  pinion  c  will  revolve  as 
many  times  as  the  number  of  leaves  borne  by  c  is  con- 
tained times  in  the  number  of  teeth  borne  by  /.  In  like 
manner,  while  the  wheel  c  revolves  once,  the  wheel  and 
pinion  b  will  revolve  as  many  times  as  the  number  of  leaves 
borne  by  b  is  contained  times  in  the  number  of  teeth 
borne  by  c.  By  combination  of  these  results,  we  see  that 
while  d  revolves  once,  #  will  have  as  many  revolutions  as 
the  product  of  the  number  of  leaves  is  contained  times  in 
the  product  of  the  number  of  teeth.  From  this  it  follows 
that  the  ratio  between  the  continued  product  of  the  cir- 
cumference (diameter  or  radius)  of  d  into  the  number  of 
leaves  on  the  several  pinions  and  the  continued  product  of 
the  corresponding  dimension  of  Z>  into  the  number  of  teeth 
on  the  several  wheels  will  be  the  ratio  between  the  dis- 
tances or  velocities  of  W  and  P,  and  therefore  the  ratio 
between  the  intensities  of  balancing  weights  or  forces. 

In  short,  the  continued  product  of  the  power,  the  cir- 
cumference of  a  and  the  number  of  teeth  on  c  and  / 
equals  the  continued  product  of  the  weight,  the  circum- 
ference of  d  and  the  number  of  leaves  on  the  pinions  c 
and  I. 

188.  Example. — Suppose  the  circumferences   of  a 
and  d  to  be  60  mm.  and  15  mm.  respectively  ;  that  I  has  9 
leaves ;   c  has  36  teeth  and   13  leaves ;  /  has  40  teeth. 
Then  will 

P  x  60  x  36  x  40  =  W  x  15  x  13  x  9. 

189.  Ways   of  Connecting  Wheels.— Wheels 
may  be  connected  in  three  ways : 

(1.)  By  the  friction  of  their  circumferences. 
(2.)  By  bands  or  belts. 


WHEEL-  WORK. 


101 


(3.)  By  teeth  or  cogs. 

The  third  of  these  methods  has  been  already  considered. 

190.  Uses  of  the  First  Two  Ways.— The  first 
method  is  used  where  no  great  resistance  is  to  be  overcome, 
but  where  evenness  of  motion  and  freedom  from  noise  are 
chiefly  desired.     It  is  illustrated  in  some  sewing-machines. 
The  second  method  is  used  when  the  follower  is  to  be  at 
some  distance  from  the  driver.     The  friction  of  the  belt 
upon  the  wheels  must  be  greater  than  the  resistance  to  be 
overcome.    It  is  illustrated  in  most  sewing-machines,  and 
in  the  spinning-wheel. 

191.  Relation   of    Power   to   Weight   De- 
termined.— The  follower  will  revolve  as  many  times 
as  fast  as  the  driver,  as  its  circumference   is  contained 
times  in  that  of  the  driver.     The  problem  of  finding  the 
distances  passed  over  in  a  given  time  by  the  power  and 
weight,  and  thence   the  relative  intensities  of  the  power 
and  the  weight,  thus  becomes  an  easy  one. 

EXEKCISES. — TJie  Wheel  and  Axle. 

Remark. — The  circumference  of  a  circle  is  3.1416  times  greater 
than  its  diameter. 


•si 
11 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

C 
o> 

1 

251bs. 
? 
23  Ibs. 
9  Kg. 
1341  Kg. 
195  Ibs. 
9 

3  Ibs. 
2  Ibs. 
49  Ibs. 
13  oz. 

i 

$ 

DIMENSIONS. 

R 

D 

c 

r 

d 

c 

y 

750  Kg. 
230  Ibs. 
153  Kg. 

9 

? 
80  Kg. 
48  Ibs. 
40  Ibs. 

9 
? 

? 

20ft. 

4ft. 
50cm. 
? 
17cm. 

15  in. 

15ft. 

12.50  m. 

9 



? 

? 

628.32  cm. 
25  in. 

4cm 

20cm. 

1m. 



16  in. 

? 
? 

? 
? 
7  in. 

10cm. 

3din. 

16  in. 

78.74  in. 

103  WHEEL-  WORK. 

12.  The  pilot-wheel  of  a  boat  is  3  feet  in  diameter  ;   the  axle,  6 
inches.     The  resistance  of  the  rudder  is  180  pounds.     What  power 
applied  to  the  wheel  will  move  the  rudder? 

13.  Four  men  are  hoisting  an  anchor  of  1  ton  weight ;  the  barrel 
of  the  capstan  is  8  inches  in  diameter.     The  circle  described  by  the 
handspikes  is  C  feet  8  inches  in  diameter.      How  great  a  pressure 
must  each  of  the  men  exert  ? 

14.  With  a  capstan,  four  men  are  raising  a  1000  pound  anchor. 
The  barrel  of  the  capstan  is  a  foot  in  diameter ;  the  handspikes 
used  are  5  feet  long  ;    friction  equals  10  per  cent  of  the  weight. 
How  much  force  must  each  man  exert  to  raise  the  anchor  ? 

15.  The  circumference  of  a  wheel  is  8  ft.;  that  of  its  axle,  16 
inches.     The  weight,  including  friction,  is  85  pounds  ;  how  great  a 
power  will  be  required  to  raise  it  ? 

16.  A  power  of  70  pounds,  on  a  wheel  whose  diameter  is  10  feet, 
balances  300  pounds  on  the  axle.     Give  the  diameter  of  the  axle. 

17.  An  axle  10  inches  in  diameter,  fitted  with  a  winch  18  inches 
long,  is  used  to  draw  water  from  a  well,    (a.)  How  great  a  power  will 

it  require  to  raise  a  cubic  foot  of  water  which  weighs  62 1  Ibs.  ?    (6.)  /  f 
How  much  to  raise  20  litres  of  water  ? 

18.  A  capstan  whose  barrel  has  a  diameter  of  14  inches  is  worked 
by  two  handspikes,  each  7  feet  long.     At  the  end  of  each  handspike 
a  man  pushes  with  a  force  of  30  pounds ;    2  feet  from  the  end  of 
each  handspike,  a  man  pushes  with  a  force  of  40  pounds  ;  required 
the  effect  produced  by  the  four  men. 

19.  How  long  will  it  take  a  horse  working  at  the  end  of  a  bar  7 
feet  long,  the  other  end  being  in  a  capstan  which  has  a  barrel  of  14 
inches  in  diameter,  to  pull  a  house  through  5  miles  of  streets,  if  the 
horse  walk  at  the  rate  of  2|  miles  an  hour  ? 

Recapitulation. — To  be  amplified  by  the  pupil  for 
review. 

DEFINITIONS. 

ADVANTAGES. 

RELATION  TO  THE  LEVER. 


WHEEL 
AND    AXLE. 


FORMULAS  AND  LAWS. 
FORMS. 

DRIVER. 
FOLLOWER. 

WHEEL    WORK.    \ 

\  USES. 
RELATION  OF  P  TO  W 


THE    PULLEY. 


103 


ECTfON  HI. 


THE    PULLEY   AND   THE    INCLINED    PLANE. 

192.  What  is  a  Pulley?--^  pulley  consists  of 
a  wheel  turning  upon  an  axis  and  having  a  cord 
passing  over  its  grooved  circumference.     The  frame 
supporting  the  axis  of  the  wheel  is  called  the  block. 

193.  A  Fixed    Pulley. — The  advantages  arising 
from  the  use  of  a  pulley  depend  upon  the  uniform  tension 
of  the  cord.     If  a  cord  be  passed  over  a 

pulley  fixed  to  the  ceiling,  a  weight  being 
at  one  end  and  the  hand  applied  at  the 
other,  the  tension  of  the  cord  will  be  uni- 
form, and  the  hand  will  have  to  exert  a 
forca  equal  to  the  weight  of  the  load.  If 
the  weight  be  moved,  the  hand  and  weight 
will  move  equal  distances.  It  is  evident, 
ihen,  that  the  fixed  pulley  affords  no 
increase  of  power,  but  only  change 
of  direction. 

194.  A  Movable  Pulley.— If  one 

end  of  the  cord  be  fastened  to  the  ceil- 
ing, the  load  suspended  from  the  pulley, 
and  the  other  end  of  the  cord  drawn  up 
by  the  hand,  it  will  be  evident,  from  the 
equal  tension  of  the  cord,  that  the  fixed 
support  carries  half  the  load  and  the  hand 
the  other  half.  It  is  also  evident  that  to 
raise  the  weight  one  foot  the  hand  must 
pull  up  two  feet  of  the  cord;  that  is  to  FIG.  52. 


FIG.  51. 


104 


THE  PULLEY. 


say,  eacli  section  of  the  cord  carrying  the  weight  must  be 
shortened  one  foot.  Thus  the  hand,  by  lifting  50  pounds 
two  feet,  is  able  to  raise  100  pounds  one  foot.  It  is  to  be 
noticed  that  we  have  here  no  creation  or  increase  of 
energy,  working  power,  but  that  we  do 
secure  an  important  transformation  of 
velocity  into  intensity. 

195.  A  Combination  of  Pul- 
leys.— By  the  use  of  several  fixed  and 
movable  pulleys  in  blocks,  the  number 
of  parts  of  the  cord  supporting  the  mov- 
able block  may  be  increased  at  pleasure. 
In  all  such  cases,  the  tension  of  the  cord 
will  be  uniform,  and  the  part  of  the  cord 
to  which  the  power  is  applied,  will  carry 
only  a  part  of  the  load.     The  value 
of  this  part  of  the  load  depends  upon 
the  number  of  sections  into  which  the 
movable  pulley  divides  the  cord. 

196.  Law   of   the   Pulley.- 

With  a  pulley  having  a  contin- 
uous cord,  a  given  power  ivill  support  a 
weight  as  many  times  as  great  as  itself  as 
there  are  parts  of  the  cord  supporting  the 
movable  Hock. 

197.   Concerning    the    Number    of 
Parts  of  the  Cord.— By  observing  the  sev- 
eral figures  of  pulleys  in  this  section,  it  will  be 
seen  that  when  the  fixed  end  of  the  cord  is  at- 
^       tached  to  the  fixed  block,  the  number  of  parts  of 
FIG.  54.   the  cord  supporting  the  weight  is  twice  the  num- 


FIG.  53. 


THE  INCLINED  PLANE.  105 

her  of  movable  pulleys  used  ;  that  whan  the  fixed  end  of 
the  cord  is  attached  to  the  movable  block  the  number  of 
parts  of  the  cord  is  one  more  than  twice  the  number  of 
movable  pulleys  used. 

198.  What  is  an  Inclined  Plane?— The  in- 

dined  plane  is  a  smooth,  hard,  inflexible  surface 
inclined  so  as  to  make  an  oblique  angle  ivith  the 
direction  of  the  force  to  be  overcome.  In  most  cases  it 
is  a  plane  surface  inclined  to  the  horizon  at  an  acute  angle, 
and  is  used  to  aid  in  the  performance  of  work  against  the 
force  of  gravity. 

199.  Resolution  of  the  Force  of  Gravity.— 

When  a  weight  is  placed  upon  an  inclined  plane,  the  force 
of  gravity  tends  to  draw  it  vertically  downward.  This 
force  may  be  resolved  into  two  forces  (§  91),  one  acting  per- 
pendicularly to  the  plane,  producing  pressure  completely 
resisted  by  the  plane,  the  other  component  acting  opposite 
to  the  direction  of  the  power  which  it  is  to  counterbalance. 
The  first  component  shows  how  much  pressure  is  exerted 
upon  the  plane ;  the  other  shows  what  force  must  be 
exerted  to  maintain  equilibrium.  The  value  of  the  second 
component  will,  plainly,  vary  with  the  direction  of  the 
power. 

200.  Three   Cases.— In  the  use  of  an  inclined  plane,  three 
cases  may  arise : 

(1.)  Where  the  power  acts  in  a  direction  parallel  to  the  length  of 
the  plane.  ' 

(2.)  Where  the  power  acts  in  a  direction  parallel  to  the  base  of  the 
plane  (generally  horizontal). 

(3.)  Where  the  power  acts  in  a  direction  parallel  to  neither  the 
length  nor  the  base  of  the  plane. 

20 1.  The  First  Case.— In  the  accompanying   figure,  let 


106 


THE  INCLINED  PLANE. 


B', 


\ 

\ 
C 

FIG.  55- 


LM  represent  a  plane  inclined  to  the  horizontal  line  LN.  Let  A 
represent  a  ball  weighing  20  Kg.  The 
problem  is  to  find  what  force  acting  in  the 
direction  LM  will  hold  it  in  equilibrium. 
The  weight  of  the  body  A  is  a  downward 
force  of  20  Kg.,  which  may  be  graphically 
represented  (§  81)  by  the  vertical  line  AC, 
20  mm.  in  length.  Any  other  convenient 
unit  of  length  might  be  used,  but  the 
scale  of  1  mm.  to  the  Kg.  being  adopted, 
it  must  be  maintained  throughout  the 
problem.  The  force  represented  by  AC 
is  resolved  into  two  components  repre- 

sented by  AD,  perpendicular  to  LM,  and  by  AB,  parallel  to  it.  The 
former  component  measures  the  pressure  to  be  resisted  by  the  plane  ; 
the  latter  component  measures  the  force  with  which  the  ball  is 
drawn  towards  L.  This  second  component  is  to  be  balanced  by  the 
equal  and  opposite  force  AB',  the  equilibrant  of  AB,  It  may  be 
proved  geometrically  that  * 

AB  i  AC  :  :  MN  :  ML.    (Olney's  Geometry,  Art.  341.) 
Careful  construction  and  measurement  will  give  the  same  result. 
But  AB,  or  rather  its  equal  AB'  ,  represents  the  power  ;  AC  repre- 
sents the  weight  ;  MN  represents  the  height  ;  and  ML,  the  length 
of.  the  plane.    Therefore, 

P  :   W  :  :  h  :  I,      or,      P  =  the  y  part  of  W. 

I/ 

2O2.  Law  for  the  First  Case.—  In  the  figure 
above,  ML  is  twice  the  length  of  MN,  and  AC  is  twice  the 
length  of  AB  or  AB'.  This  indi- 
cates that  a  force  of  10  Kg.  acting  in 
the  direction  LM  would  hold  the 
ball  in  equilibrium.  This  result  may 
be  easily  verified  by  experiment. 
We  may  therefore  establish  the  fol- 
lowing  law  :  'JV/ien  a  given  power 
acts  parallel  to  tfie  plane,  it  will 
support  a  weight  as  many  times  as  great  as  itself  as 
the  length  of  the  plane  is  times  as  great  as  Us  verti- 
cal height. 


20  Kg. 


10  Kg. 


pIG  56> 


THE  INCLINED  PLANE 


107 


203.  Law  for  the   Second  Case.— By  resolving 
the  force  of  gravity,  or  by  experi- 
ment,  the  following  law  may  be 

established :  When  a  given  power 
acts  parallel  to  the  base,  it  luill 
support  a  weight  as  many 
times  as  great  as  itself  as  the 
hoHzontal  base  of  the  plane  is 
times  as  great  as  its  vertical 
height. 

204.  The    Third    Case.— For  the  third  case,  the  power 
acting  in  a  direction  parallel  to  neither  the  length  nor  the  base  of 
the  plane,  no  law  can  be  given.    The  ratio  of  the  power  to  the 
weight  may  be  determined  by  resolving  the  force  of  gravity,  as 
above  explained,  the  construction  and  measurement  being  carefully 
done. 

EXERCISES. 

Remark. — The  first  problem  may  be  read  : 

(a.)  In  a  system  of  pulleys,  the  weight  being  supported  by  two 
sections  of  the  cord,  a  power  of  25  Ibs.  will  support  what  weight  ? 

(&.)  In  an  inclined  plane,  the  power  acting  in  the  direction  of  the 
length  of  the  plane,  the  height  of  the  plane  being  3  ft.,  what  must 
be  the  length  that  the  same  power  may  support  the  same  weight  ? 


No. 

POWER. 

WEIGHT. 

PULLET. 

INCLINED  PLANE. 

Cords. 

Height. 

Length. 

Base. 

Case. 

1 

2 
3 

4 
5 
6 
7 
8 
9 
10 

25  Ibs. 
13  Kg. 
12  oz. 
250  g. 
? 
15  cwt. 
20  g. 
500  Kg. 
? 
75  Ibs. 

? 
78  Kg. 
? 
2  Kg. 
-    350  Ibs. 
3T. 
IHg. 
? 
540  Ibs. 
100  Ibs. 

2 
? 
8 
? 

7 

9 

? 

8 
9 

3ft. 
? 
? 
1dm. 
? 
4rds. 

9 

? 

39.37  in. 
3vds. 

? 
12m. 

1 
1 
2 
1 
2 
1 
2 
1 
1 
2 

2  ft. 

? 
? 

49  ft. 

10m. 

24m. 
?m. 

? 

? 

108  THE  INCLINED  PLANE. 

11.  With  a  fixed  pulley,  what  power  will  support  a  weight  of  50 
pounds  ? 

12.  With  a  movable  pulley,  what  power  will  support  a  weight  of 
50  pounds  'I 

13.  What  is  the  greatest  effect  of  a  system  of  3  movable  and  4 
fixed  pulleys,  the  power  applied  being  75  pounds  ? 

14.  With  a  system  of  5  movable  pulleys,  one  end  of  the  rope 
being  attached  to  the  fixed  block,  what  power  will  raise  a  ton  ?    £|/fc 

15.  If  in  the  system  mentioned  in  the  problem  above,  the  rope  be 
attached  to  the  movable  block,  what  power  will  raise  a  ton  ? 

16.  With  a  pulley  of  6  sheaves  in  each  block,  what  is  the  least 
power  that  will  support  a  weight  of  1,800  pounds,  allowing  ^"for 
friction  ?    What  will  be  the  relative  velocities  of  P  and  W  ? 

17.  Figure  a  set  of  pulleys  by  which  a  power  of  50  pounds  will 
support  a  weight  of  250  pounds. 

18.  The  height  of  an  inclined  plane  is  one-fifth  its  horizontal 
base.    A  globe  weighing  250  Kg.  is  supported  in  place  by  a  force 
acting  at  an  angle  of  45°  with  the  base.    The  pressure  of  the  globe 
upon  the  plane  is  less  than  250  Kg.     By  construction  and  measure- 
ment, determine  the  intensity  of  the  supporting  force. 

19.  With  the  conditions  as  given  in  the  last  problem,  except  that 
the  pressure  of  the  globe  upon  the  plane  is  more  than  250  Kg.,  de- 
termine the  intensity  of  the  supporting  force. 

20.  The  base  of  an  inclined  plane  is  10  feet ;  the  height  is  3  feet. 
What  force,  acting  parallel  to  the  base,  will  balance  a  weight  of 
2  tons'? 

21.  An  incline  has  its  base  10  feet ;  its  height,  4  feet :  how  heavy  a 
ball  will  50  pounds  power  roll  up  f 

22.  How  great  a  power  will  be  required  to  support  a  ball  weighing 
40  pounds  on  an  inclined  plane  whose  length  is  8  times  its  height  ? 

23.  A  weight  of  800  pounds  rests  upon  an  inclined  plane  8  feet 
high,  being  held  in  equilibrium  by  a  force  of  25  pounds  acting 
parallel  to  the  base.     Find  the  length  of  the  plane. 

24.  A  load  of  2  tons  is  to  be  lifted  along  an  incline.     The  power 
is  75  pounds  ;  give  the  ratio  of  the  incline  which  may  be  used. 

25.  A  1500  pound  safe  is  to  be  raised  5  feet.     The  greatest  power 
that  can  be  applied  is  250  pounds.     Give  the  dimensions  of  the 
shortest  inclined  plane  that  can  be  used  for  that  purpose. 

Recapitulation. — To  be  amplified  by  the  pupil  for 
review. 


THE    WEDGE. 


109 


PULLEY. 


DEFINITION. 

f  FIXED. 
KINDS.  <!  MOVABLE. 

[  COMBINATIONS. 

LAW. 

RELATION  between  the  number  of  pulleys  and  the 
number  of  parts  of  the  cord. 

(  DEFINITION. 

INCLINED  ]  FORCE  OF  GRAVITY 
PLANE,    j          RESOLVED. 


IV. 


THE  WEDGE,  SCREW,  COMPOUND  MACHINES,  AND 
FRICTION. 

2O5.  What  is   a  Wedge?— A  wedge  is  a  mov- 
able   inclined,    plane    in 
which   the   power  gener- 
ally acts  parallel  to  the 
base. 


2O6.  Its  Use.— This 
wedge  is  used  for  moving 
great  weights  short  dis- 
tances. The  law  is  the  FlG-  58. 
same  as  for  the  corresponding  inclined  plane.  A  common 
method  of  moving  bodies  is  to  place  two  similar  wedges, 
with  their  sharp  edges  overlapping,  under  the  load. 
Simultaneous  blows  of  equal  force  are 
struck  upon  the  heads  of  the  wedges. 
In  this  case,  the  same  force  must  be 
used  upon  each  wedge  as  if  only  one 
FIG.  59.  were  used,  but  the  power  being  doubled 


110 


THE  SCREW. 


FIG.  60. 


and  the  weight  remaining  the  same,  the  distance  moved  is 
twice  as  great  as  when  only  one  wedge  is  used. 

207.  A  More   Common  Use. — A  more  com- 

mon kind  of  wedge  is  that  of  two  in- 
clined planes  united  at  their  liases.  Such 
wedges  are  used  in  splitting  timber,  stone,  etc. 
The  power  is  given  in  repeated  blows  instead 
of  continued  pressure.  For  a  wedge  thus  used 
no  definite  law  of  any  practical  value  can  be 
given,  further  than  that,  with  a  given  thick- 
ness, the  longer  the  wedge  the  greater  the  gain 
in  intensity  of  power. 

208.  What  is  a  Screw?— A  Screw  is  a  cylin- 
der, generally   of  wood 

or  metal,  ivith  a  spiral 
groove  or  ridge  winding 
about  its  circumference. 
The  spiral  ridge  is  called 
the  thread  of  the  screw. 
The  thread  works  in  a  nut, 
within  which  there  is  a 
corresponding  spiral  groove 
to  receive  the  thread. 

(a.)  The  power  is  used  to  turn  the  screw  within  a  fixed  nut,  or  to 
turn  the  nut  about  a  fixed  screw.  In  cither  case,  a  lever  or  wheel 
is  generally  used  to  aid  the  power.  Every  turn  of  the  screw  or  nut 
either  pushes  forward  the  screw  or  draws  back  the  nut  by  exactly 
the  distance  between  two  turns  of  the  thread,  this  distance  being 
measured  in  the  direction  of  the  axis  of  the  screw.  The  weight  or 
resistance  at  W  is  moved  this  distance,  while  the  power  at  P  moves 
over  the  circumference  of  a  circle  whose  radius  is  PF.  The  differ- 
ence between  these  distances  is  generally  very  great.  Hence  this 
machine  affords  great  intensity  of  power  with  a  corresponding  loss 
of  velocity. 


FIG.  61. 


COMPOUND    MACHINES. 


Ill 


209.  Law  of  the   Screw.— The  second  general 
law  of  machines  (§  167,  [2])  may  be  adapted  to  our  present 
purpose  as  follows :   With  the  screw,  a  given  power  wi% 
support  a  weight  as  many  times  as  great  as  itself  as 
the  circumference  described  l)ij  the  power  is  times  as 
great  as  the  distance  between  two  adjoining  turns 
of  the  thread. 

210.  The   Endless   Screw.—  An  endless  screw 
is  one  whose  thread  acts  on  the  teeth  of  a  wheel. 
The  screw  has  a  rotary  but  no 

lengthwise  motion.  As  the  han- 
dle is  turned,  the  thread  catches 
the  teeth  and  turns  the  wheel. 
The  wheel  moves  one  tooth  for 
every  turn  of  the  handle.  Suc- 
cessive teeth  are  caught  as  others 
pass  out  of  reach.  A  continuous 
motion  is  thus  produced  ;  hence 
the  name  "  endless  screw."  The 
figure  will  aid  in  the  application  of  the  second  general  law 
of  machines  to  determine  the  ratio  between  the  weight  and 
the  power. 

211.  Compound  Machines.— We  have  now  con- 
sidered each  of  the  six  traditional  simple  machines.     One 
of  these  may  be  made  to  act  upon  another  of  the  same 
kind,  as  in  the  case  of  the  compound  lever  or  wheel-work ; 
or  upon  another  of  a  different  kind,  as  in  the  case  of  the 
endless  screw.     When  any  two  or  more  of  these  machines 
are  combined,  the  effective  force  may  be  found  by  comput- 
ing the  effect  of  each  separately  and  then  confounding 
them  ;  or  by  finding  the  weight  that  the  given  power  will 


FIG.  62. 


112  FRICTION. 

support,  using  the  first  machine  alone,  considering  the 
result  as  a  new  power  acting  upon  the  second  machine, 
and  so  on.  j 

212.  What  is  Friction  ?— The  chief  impediment 
to  the  motion  of  machinery  arises  from  friction,  which  may 
be  defined  as  the  resistance  which  a  moving   body 
meets  with  from  the  surface  on  which  it  moves. 

213.  The  Cause  of  Friction. — It  is  impossible, 
by  any  known  means,  to  produce  a  perfectly  smooth  sur- 
face.    Even  a  polished   surface  contains  minute  projec- 
tions which  fit  into  corresponding  depressions  on  the  cor- 
responding surface.     To  produce  motion  of  one  surface  on 
the  other,  these  projections  must  be  lifted  out,  bent  down, 
or  broken  off. 

214.  Eight   Facts  Concerning   Friction.— 

The  following  facts  have  been  determined  by  experiment, 
and  may  be  easily  illustrated  in  the  same  way : 

(1.)  Friction  is  greatest  at  the  'beginning  of  motion. 
After  surfaces  have  been  in  contact  for  some  time, 
so  that  the  projections  of  one  have  had  opportunity 
to  sink  deeper  into  the  depressions  of  the  other,  the 
resistance  offered  by  friction  is  considerably  in- 
creased. Every  teamster  and  street-car  driver  is 
familiar  with  the  fact. 

(2.)  Friction  increases  with  the  roughness  of  the 
surfaces. 

(3.)  Friction  is  greater  between  soft  bodies  than 
hard  ones. 

(4.)  Friction  is  nearly  proportional  to  pressure. 
(a.)  Place  a  brick  upon  a  horizontal  board.     Around  it  fasten  one 

end  of  a  cord  and  pass  the  other  end  over  a  pulley  so  that  it  may 

hang  vertically.     Add  just  weights  enough  to  keep  the  brick  in 


FRICTION. 


113 


motion  after  it  is  started.  The  weights  measure  the  friction.  Place 
a  second  similar  brick  upon  the  first ;  the  moving  force  must  be 
doubled.  Place  another  similar  brick  upon  the  other  two  ;  the 
original  moving  force  must  be  tripled. 

(5.)  Friction  is  not  affected  by  extent  of  surface 
except  within  extreme  limits.  In  the  case  of 
the  brick  above  mentioned,  the  moving  force  will 
be  the  same  whether  the  brick  lie  on  its  broad  face 
or  on  its  side. 

(6.)  Friction  is  greater  between  surfaces  of  the 
same  material  than  between  those  of  differ- 
ent kinds. 

(a.)  Bodies  of  the  same  material  have  the  same  molecular  struc- 
ture (§  10,  a).  Hence  their  little  projections  and  cavities  mutually 
fit  each  other  as  would  the  teeth  of  similar  saws.  A  very  little  re- 
flection will  show  that  the  element  of  similarity  in  molecular  struc- 
ture (just  as  with  the  saws)  is  very  important  in  determining  the 
amount  of  friction.  For  this  reason,  the  axles  of  railway  cars  being 
made  of  steel,  the  "  boxes  "  in  which  they  revolve  are  made  of  brass 
or  other  different  metal.  Hence  the  advantages  of  a  watch  "full- 
jewelled,"  and  hence  the  swiftness  of  the  skillful  skater. 

(7.)  Rolling  friction  is  less  than  sliding  friction. 

(8.)  Friction  is  diminished  by  polishing  or  lubri- 
cating the  surfaces.  An  unequalled  example  of 
friction  reduced  to  its  minimum  is  in  the  case  of 
the  joints  of  animals. 

EXERCISES. — The  Screw. 


No. 

P. 

W. 

C. 

d. 

No. 

P. 

W. 

C. 

d. 

1 

15  Ibs. 

? 

10  in. 

iin. 

8 

? 

2500  Kg. 

2.5m. 

1  cm. 

2 

5  Kg. 

9 

8m. 

1  cm. 

9 

4  oz. 

Gibs. 

/if 

7  in. 

3 

lib. 

:  r 

75  in. 

Jta. 

10 

fibs. 

7874  Ibs. 

1  m. 

lin. 

4 

! 

480  Ibs. 

15  in. 

lin. 

11 

3  Kg. 

300  Kg. 

20  cm. 

? 

5 

20  Ibs. 

800  Ibs. 

^0'-v-' 

|in. 

12 

3  oz. 

864  oz. 

JL*  * 

lin. 

6 

25  Ibs. 

? 

3ft. 

lin. 

13 

100  Ibs. 

•i 

10  ft, 

fin. 

7 

2  Ibs. 

192  Ibs. 

4ft. 

ty: 

14 

100  Ibs. 

jffrtl  loft. 

*in. 

114  THE  SCREW. 

15.  A  book-binder  has  a  press;  the  threads  of  its  screw  are  I  in.  apart-, 
the  nut  is  worked  by  a  lever  which  describes  a  circumference  of 
8  ft.     How  great  a  pressure  will  a  power  of  15  Ibs.  applied  at  the  end 
of  the  lever  produce,  the  loss  by  friction  being  equivalent  to  240  Ibs.  ?  > 

16.  A  screw  has  11  threads  for  every  inch  in  length.     If  the 
lever  is  8  inches  long,  the  power,  50  pounds,  and  friction  is  -J  of  the 
energy  used,  what  resistance  may  be  overcome  by  it  ? 

17.  A  screw  with  threads  1]  in.  apart  is  driven  by  a  lever  4*  ft. 
long  ;  what  is  the  ratio  of  the  power  to  the  weight  ?  (See  Appendix  A. ) 

18.  How  great  a  pressure  will  be  exerted  by  a  power  of  15  Ibs. 
applied  to  a  screw  whose  head  is  one  inch  in  circumference  and 
whose  threads  are  £  inch  apart  ? 

19.  At  the  top  of  an  inclined  plane  which  rises  1  ft.  in  20  is  a  wheel 
and  axle.    Radius  of  wheel =2 £  ft. ;  radius  of  axle— 4|-  in.    What  load 
may  be  lifted  by  a  boy  who  turns  the  wheel  with  a  force  of  25  Ibs.  ? 

20.  The  crank  of  an  endless  screw  whose  threads  are  an  inch 
apart  describes  a  circuit   of  72  inches.     The  screw  acts  on  the 
toothed  edge  of  a  wheel  60  inches  in  circumference.     On  the  axle 
of  this  wheel,  which  is  10  inches  in  circumference,  is  wound  a  cord 
which  acts  upon  a  set  of  pulleys,  3  in  each  block.     The  effect  of  the 
pulleys  is  exerted  upon  the  wheel  of  a  wheel  and  axle.    The  diam- 
eters of  the  wheel  and  of  the  axle  are  4  ft.  and  6  inches  respec- 
tively.   What  weight  on  the  wheel  and  axle  may  be  lifted  by  a 
force  of  25  Ibs.  at  the  crank,  allowing  for  a  loss  of  -*-  by  friction  ? 

21.  An  endless  screw  which  is  turned  by  a  wheel  10ft.  in  circum- 
ference acts  upon  a  wheel  having  81  teeth  ;  this  wheel  has  an  axle 
18  inches  in  circumference  ;  the  power  is  75  Ibs.     Find  the  value  of 
the  weight  that  may  be  suspended  from  the  axle. 

22.  In  moving  a  building  the  horse  is  attached  to  a  lever  7  feet 
long,  acting  on  a  capstan  barrel  11  inches  in  diameter  ;  on  the  barrel 
winds  a  rope  belonging  to  a  system  of  2  fixed  and  3  movable  pul- 
leys.    What  force  will  be  exerted  by  500  pounds  power,  allowing 
|  for  loss  by  friction  ? 

Recapitulation. — To  be  amplified  by  the  pupil  for 
review. 

WFnPF         J  DEFINITION. 

WhUbt.        -j  TWO  USES  AND  THE  LAW  FOR  EACH. 

(  DEFINITION. 
SCREW.        -I  LAW. 

(  ENDLESS  SCREW  ;  ITS  ADVANTAGES  ;  RELATION  OF  P  TO  W. 

COMPOUND  MACHINES  ;  RELATION  OF  P  TO  w. 

(DEFINITION. 

FRICTION.^  CAUSE. 

EIGHT  FACTS. 


REVIEW.  115 


REVIEW  QUESTIONS  AND  EXERCISES. 

I.  (a.}  What  is  a  machine  ?    (6.)  What  is  a  machine  good  for  ? 
(c.)  State  the  general  laws  of  machines  andf(d)  illustrate  by  the 
pulley      ^&<M<&'tc^ 

i  2.  (a.)  What  are  the  arms  of  a  lever  ?  (6.)  What  is  meant  by  the 
moment  of  a  force  ?  (c.)  Illustrate  the  equality  of  moments  in  ma- 
chines by  the  wheel  and  axle. 

3.  (a.)  What  are  the  respective  advantages  to  be  gained  by  the 
several  classes  of  levers?  J  (&.)  Explain  the  advantage  gained  .by  a 
claw  hammer  in  drawing  a  nail,    (c.)  What  is  meant  by  double 
weighing  ? 

4.  With  a  lever  of  given  length,  in  which  class  will  a  given 
power  yield  the  greatest  intensity  of  effect  ? 

5.  (a.)  To  what  kind  of  a  lever  is  ordinary  clock-work  analogous? 
(&.)  Show  why. 

6.  (a.)  Does  it  require  more  work  to  lift  a  barrel  of  flour  into  a 
wagon  four  feet  high  than  to  place  it  there  by  rolling  it  up  a  plank 
12  feet  long  ?    (6.)  Show  why. 

7.  (a.)  Give  the  static  law  for  the  inclined  plane  when  the  power 
acts  parallel  to  the  plane.     (&.)  When  it  acts  parallel  to  the  horizon, 
(c.)  Figure  a  system  of  pulleys  by  means  of  which  a  weight  of  5 
pounds  will  support  a  weight  of  25  pounds. 

8.  («.)  Figure  a  system  of  4  movable  pulleys  by  means  of  which. 
a  weight  of  3  Ibs.  will  support  a  weight  of  27  Ibs.     (&.)  Deduce 
the  formula  for  the  screw  from  one  of  the  general  laws  of  machines. 

9.  (a.)  In  raising  a  boy  from  a  deep  well  by  means  of  a  common 
rope  and  pulley,  what  disadvantages  arise  from  friction  ?   (6.)  What 
immense  advantage  ? 

10.  (a.)  Explain  the  cause  of  friction.    (&.)  Why  is  friction  between 
iron  and  iron  greater  than  that  between  iron  and  brass? 

II.  (a.)  How  may  the  centre  of  gravity  of  a  ring  be  determined  ? 
(&.)  What  is  the  value  in  inches  of  the  metric  unit  of  length? 

12.  A  body  moving  with  an  energy  of  20  foot-pounds,  strikes  the 
end  of  the  arm  of  a  lever  of  the  first  class,  four  feet  from  the 
fulcrum,    (a.)  How  many  foot-pounds  will  be  exerted  by  the  other 
end  of  the  lever,  6  feet  from  the  fulcrum  ?    (&.)  How  far  would  it 
raise  a  weight  of  4  pounds  ? 

13.  Deduce  the  static  law  for  the  inclined  plane,  first  case,  by 
resolution  of  the  force  of  gravity. 

14.  (a.)  What  force  is  necessary  to  overturn  a  body  ?    (&.)  What 
difference  between  the  forces  producing  uniform  and  accelerated 
velocities?    (c.)  Show  that  the  screw  is  a  modified  inclined  plane. 


IV. 


LIQUIDS. 


ECTfON  I, 


HYDROSTATICS. 

215.  Incompressibility  of  Liquids. — Liquids 
are  nearly  incompressible.  A  pressure  of  15  pounds  to 
the  square  inch  compresses  distilled  water  only  2  6  010  0  0- 
part  of  its  volume ;  it  compresses 
mercury  only  one-tenth  as  much. 
This  virtual  in  compressibility  of 
liquids  is  of  the  highest  practical 
importance. 

V216.  Transmission  of 
Pressure.— Fluids  can  trans- 
mit pressure  in  every  direc- 
tion, upward,  downward,  and 
sidewise  at  the  same  time. 

(a.)  This  property  of  liquids  may  be 
illustrated  by    the    apparatus    repre- 
«    sented   in   Fig.   G3.      The  globe  and 
cylinder  being  filled  with  water  and 
the    several    openings    in   the    globe 
FIG.  63.  closed  by  corks,  a  piston  is  pushed 


HYDROSTATICS. 


11? 


FIG.  64. 


down  the  cylinder.  The  pressure  thus  received  and  transmitted  by 
the  confined  water  expels  the  cork  and  throws  a  jet  of  water  from 
each  aperture.  (See  Appendix  D.) 

(&.)  The  explanation  of  this  property  of  fluids  may  be  seen  by 
reference  to  Fig.  64,  representing  five  molecules  of  any  fluid.  If  a 
downward  pressure  be  applied  to  1,  it 
will  force  2  toward  the  right  and  3  tow- 
ard the  left,  thus  forming  lateral  pres- 
sure. When  thus  moved,  3  will  force  4 
upward  and  5  downward.  Owing  to  the 
freedom  with  which  the  molecules  move 
on  each  other,  there  is  no  loss  by  friction, 
and  the  downward  pressure  of  5,  the 
upward  pressure  of  4,  and  the  lateral 
pressure  of  2,  will  each  equal  the  pres- 
sure exerted  by  1.  It  makes  no  difference  with  the  fact,  whether 
the  pressure  exerted  by  1  was  the  result  of  its  own  weight  only, 
this  weight  together  with  the  weight  of  overlying  molecules,  o* 
both  of  these  with  still  additional  forces. 

217.  Pascal's    Law. — Pressure    exerted    any- 
where   upon    a    mass    of 

liquid  is  transmitted,  un- 
diminished  in  all  direc- 
tions, and  acts  with  the 
same  force  upon  all  equal 
surfaces  and  in  a  direc- 
tion at  right  angles  to 
those  surfaces. 

218.  An  Argument  from 
Pascal's  Law. — Fill  with  water 
a  vessel  of  any  shape,  having  in 
its  sides  apertures  whose  areas  are 
respectively    as  1,  2  and    3,    each 

aperture  being  closed  with  a  piston.  Suppose  the  pistons  to  move 
without  friction  and  the  water  to  have  no  weight ;  then  there  will 
be  no  motion.  Suppose  that  the  piston  whose  area  is  represented 
by  1  rests  upon  1000  molecules  of  the  water  ;  then  will  the  piston 
at  2  rest  upon  2000,  and  that  at  3  upon  3000  molecules  of  water. 
If  now  a  pressure  of  one  pound  be  applied  to  the  piston  at  1,  this 


FIG.  65. 


118 


HYDROSTATICS. 


FIG.  66. 


pressure  is  distributed  among  the  1000  molecules  upon  which  it 
presses.  Owing  to  this  freedom  of 
motion,  these  molecules  will  transmit 
this  pressure  to  those  adjacent,  and 
these  to  those  beyond,  until  every 
molecule  of  water  in  the  vessel  exerts 
a  pressure  equal  to  that  exerted  upon 
any  one  of  the  molecules  upon  which 
the  pressure  was  originally  exerted, 
i.  e.j  every  thousand  molecules  in  the 
vessel  will  exert  a  force  of  one  pound. 
Then  will  the  2000  molecules  at  2 
exert  a  force  of  two  pounds  and  the 

3000  molecules  at  3  will  exert  a  force  of  three  pounds. 

<,  219,  An  Important  Principle.— The  foregoing 
argument  may  be  summed  up  as  follows:  When  fluids 
are  subjected  to  pressure,  the  pressure  sustained  by 
any  part  of  the  restraining  surface  is  proportional 
to  its  area. 

22O.  Experimental  Proof. — The  above  principle, 
which  we  deduced  from  Pascal's  law,  may  be  verified  by  ex- 
periment. Provide  two  com- 
municating tubes  of  unequal 
sectional  area.  When  water  is 
poured  into  these, it  will  stand 
at  the  same  height  in  both 
tubes.  If  by  means  of  a  piston 
the  water  in  the  smaller  tube 
be  subjected  to  pressure,  the 
pressure  will  force  the  water 
back  into  the  larger  tube  and 
raise  its  level  there.  To  prevent 
this  result,  a  piston  must  be  ' 

fitted  to  the  larger  tube  and  held  there  with  a  force  as 
many  times  greater  than  the  force  acting  upon  the  other 


FIG.  67. 


H  YDR  OSTA  TICS. 


119 


piston  as  the  area  of  the  larger  piston  is  times  greater  than 
the  area  of  the  smaller  one.  If,  for  example,  the  smaller 
piston  have  an  area  of  1  sq.  cm.  and 
the  larger  piston  an  area  of  16  sq. 
cm.,  a  weight  of  1  Kg.  may  he  made 
to  support  a  weight  of  1C  Kg. 

221.  Pascal's  Experiment. 
— Pascal  firmly  fixed  a  very  narrow 
tuhe  about  30  ft.  high  into  the  head 
of  a  stout  cask.  He  then  filled  the 
cask  and  tube  with  water.  The 
weight  of  the  small  amount  of 
water  in  the  tube,  producing  a  pres- 
sure as  many  times  greater  than 
itself  as  the  inner  surface  of  the 
cask  was  times  greater  than  the 
sectional  area  of  the  tube,  actually 
^^^^^^  burst  the  cask. 

FIG.  68.  222.   The   Hydro- 

static Bellows. — The  hydrostatic  bellows 
consists  of  two  boards  fastened  together  by 
a  broad  band  of  stout  leather,  and  a  small 
vertical   tube  communicating  with  the  in- 
terior.   If  the  tube  have  a  sectional  area  of  1 
sq.  cm.,  the  downward  pressure  at  5,  its  base, 
will  be  one  gram  ibr  every 
centimeter  of  depth  of  water 
in  the  tube.     If  the  upper 
board,  B,  have  a  surface  of 
1000  sq.  cm.  exposed  to  the 
water  in  the  bellows,  it  will 
be  pressed  upward  with   a  FIG.  69. 


120 


HYDROSTATICS. 


force  of  1000  g.  for  every  gram  of  downward  pressure  at  b. 
If  the  tube  be  2  meters  high  the  downward  pressure  at  E 
will  be  200  g.,  and  the  upward  pressure  exerted  on  B  will 
be  200  g.  x  1000  =  200,000  g.  or  200  Kg. 


223.  The  Hydrostatic  Press.— The  hydrostatic 
press,  often  called  the  Hydraulic,  or  Bramah's  press,  acts 
upon  the  same  principle.  It  is  represented  in  perspective 
by  Tig.  70  and  in  section  by  Fig  71.  Instead  of  the 
downward  pressure  produced  by  the  weight  of  the  water 
in  the  tube,  pressure  is  produced  by  the  force-pump.  In- 
stead of  the  two  boards  and  the  leather  band,  a  large. 


HYDROSTATICS. 


121 


FIG.  71. 

strong  reservoir  and  a  piston,  working  water-tight,  are 
used.  The  substance  to  be  pressed  is  placed  between  K, 
the  head  of  the  piston,  and  an  immovable  plate  MN.  The 
reservoir  and  the  cylinder  of  the  pump  are  connected 
by  the  tube  d.  By  the  action  of  the  pump,  the  water  in 
the  cylinder  A  is  subjected  to  pressure,  and  this  pressure 
is  transmitted  undiminished  to  the  water  in  B.  According 
to  the  law  given  in  §  219,  the  power  exerted  upon  the 
lower  surfaces  of  the  two  pistons  is  proportional  to  their 
respective  areas.  But  the  force  exerted  by  the  water  upon 
the  under  surface  of  the  piston  in  the  pump  is  the  same  as 
the  force  exerted  upon  the  water  by  that  piston,  (equality 
of  action  and  reaction).  The  piston  a  is  generally  worked 
by  a  lever  of  the  second  class,  resulting  in  a  still  further 
gain  of  intensity  of  power.  If  the  power  arm  of  the  lever 
be  ten  times  as  long  as  the  weight-arm,  a  power  of  50  Kg. 
at  the  end  of  the  lever  will  exert  a  pressure  of  500  Kg. 
upon  the  water  in  A.  If  the  piston  in  A  have  a  sectional 
area  of  1  sq,  cm.  and  the  piston  in  B  have  an  area  of  500 
6 


122 


HYDROSTATICS. 


sq.  cm.,  then  the  pressure  of  500  Kg.  exerted  by  the  small 
piston  will  produce  a  pressure  of  500  Kg.  x  500  =  250,000 
Kg.  upon  the  lower  surface  of  the  large  piston.  Hence 
the  following  rule : 

v\xN 
^Multiply  the  pressure  exerted  by  the  piston  of  the 

pump  by  the  ratio  between  the  sectional  areas  of 
the  two  pistons. 

(a.)  The  accompanying  figure  shows  a  device  due  to  Ritchie  of 
Boston.  It  consists  of  a  base  B  ;  a  sliding  platform  P  guided  by  two 
vertical  pillars  ;  a  bellows-formed  rubber  bag 
connecting  the  base  and  platform  ;  and  a  bag  or 
flask  F,  fitted  with  a  cap  and  cork.  The  flask  is 
connected  with  the  base  by  flexible  tubing.  A 
weight  W  is  placed  upon  the  platform.  Fill 
the  globe  with  water,  and  elevate  it ;  the  pres- 
sure of  the  column  will  force  the  water  into  the 
bellows,  raising  the  weight ;  lower  the  globe, 
and  the  weight  will  force  the  water  back 
into  it. 

224=.  Liquid  Pressure  Due  to 
Gravity.— The  pressure  exerted  by 
liquids,  on  account  of  their  weight,  may 
be  downward,  upward,  or  lateral.  Pres- 
sure in  any  other  direction  may  be  re- 
solved into  two  of  these.  We  shall  now 
briefly  consider  these  three  kinds  of 
liquid  pressure. 


FIG.  72. 


225.  Downward  Pressure. — Tlie  pressure  on 
the  bottom  of  a  vessel  containing  a  liquid,  is  in- 
dependent of  the  quantity  of  the  liquid  or  the 
shape  of  the  vessel,  but  depends  upon  the  depth 
and  density  of  the  fluid  and  the  area  of  the 
bottom. 


HYDROSTATICS. 


123 


(a.)  Pascal  contrived  a  neat  experiment  to  verify  this  principle. 
The  apparatus  consists  of  a  wooden  support  carrying  a  ring  into 
which  may  be  screwed  any  one  of  three  vessels,  one  cylindrical,  one 
widening  upward  and  one  narrowing  upward,  straight  or  bent.  On 
the  lower  side  of  the  ring  is  a  plate  a,  supported  by  a  thread  from 


FIG.  73. 

one  end  of  an  ordinary  balance.  The  other  end  of  the  balance 
carries  a  scale-pan.  Weights  in  the  scale-pan  hold  the  plate  a, 
against  the  ring  with  a  certain  force.  Water  is  carefully  poured 
into  M  until  the  pressure  forces  off  the  plate  and  allows  a  little 
of  the  water  to  escape.  A  rod  o  marks  the  level  of  the  liquid 
when  this  takes  place.  Repeating  the  experiment  with  the  same 
weights  in  the  scale-pan,  and  either  P  or  Q  in  the  place  of  M, 
the  plate  will  be  detached  when  the  water  has  reached  the  same 
height  although  the  quantity  of  water  is  much  less. 

226.  Rule  for  Downward  Pressure.— When 
the  cylindrical  vessel,  mentioned  in  the  last  paragraph,  is 
filled,  it  is  evident  that  the  downward  pressure  is  equal  to 
the  weight  of  the  contained  liquid.  It  is  further  evident 


124 


HYDROSTATICS. 


that  the  weight  of  the  counterpoise  in  the  scale-pan,  the 
weight  of  the  liquid  contained  in  P,  and  the  downward 
pressure  exerted  on  the  plate  by  the  liquid  contained  in 
M,  P,  or  Q  are  equal.  We  therefore  deduce  the  following 
rule: 

To  find  the  downward  pressure  on  a  horizontal 
surface,  find  the  weight  of  an  imaginary  column 
of  the  given  liquid,  ivhose  base  is  the  same  as  the 
given  surface,  and  whose  altitude  is  the  same  as 
the  depth  of  the  given  surface  below  the  surface 
of  the  liquid. 

Note.^—A  cubic  foot  of  water  weighs  about  1000  ounces,  624 
pounds  (more  exactly  62.42  Ibs.). 


.  Upward  Pressure.  —  Some  persons  have  dif- 
ficulty in  understanding  that  liquids  have  upward  pres- 

sure. This  upward  pressure  may 
be  illustrated  as  follows  :  Take  a 
glass  tube  open  at  both  ends,  hav- 
ing at  its  lower  end  a  glass  or  mica 
disc  supported  from  its  centre 
by  a  thread.  If  this  apparatus 
be  placed  in  water,  the  tube 
being  vertical,  the  upward  pres- 
sure of  the  water  will  hold  tbe 
disc-  in  its  place.  If  the  disc  does 
not  accurately  fit  the  end  of  the 
tube,  water  will  be  forced  into  the 
tube,  and  gradually  fill  it  from 
below.  If  the  disc  does  fit  accu- 
rately, as  is  desirable",  pour  water 
carefully  into  the  tube.  In  either  case,  the  disc  will  be 


HYDR  OSTA  TICS. 


125 


held  in  place  against  the  force  of  gravity  until  the  level  of 
the  water  within  the  tube  is  very  nearly  the  same  as  that 
in  the  outer  vessel.  The  disc  will  not  fall  until  the  weight 
of  the  water  in  the  tube  plus  the  weight  of  the  disc  equals 
the  upward  pressure.  £0I& 

Note. — A  lamp-chimney  answers  the  purpose  of  this  experiment. 
On  the  glass  disc  pour  a  little  fine  emery  powder,  and  on  this  rub 
the  end  of  the  lamp-chimney  until  they  fit  accurately.  The  string 
may  be  fastened  to  the  disc  with  wax. 

22S.  Rule  for  Upward  Pressure.— To  find 
the  upward  pressure  on  any  horizontal  surface, 
•find  the  weight  of  an  imaginary  column  of  the 
given  liquid  whose  base  is  the  same  as  the  given 
surface,  and  whose  altitude  is  the  same  as  the 
depth  of  the  given  surface  below  the  surface  of 
the  liquid. 

229.  The  Hydrostatic  Paradox.— It  may  seem 
strange  at  first  thought  that  vessels  whose  bottoms  are 
subjected  to  equal  pressure,  like  those  represented  in  Fig. 
75,  do  not  exert  equal  pressures  upon  the  stand  supporting 
tli em ;  in  other  words,  that  they  do  not  weigh  the  same. 
The  difficulty  will  be  removed  by  remembering  that  the 
pressure  on  the  bottom  of  the  vessel  is  only  one  of 
the  elements  which  combine  to  produce  the  pres-* 
sure  upon  the 

stand.     By  refer-  C  L 1  D    c|| — K s I  D    K  c 

ence  to  the  figure, 
which  represents 
three  vessels  of  un- 
equal capacity  but 
having  equal  pres- 
sures upon  the  bot- 


126 


HYDROSTATICS. 


torn,  it  will  be  seen  that  the  weight  may  be  the  resultant 
of  several  forces,  compounded  according  to  the  first  and 
second  cases  specified  in  §  80. 

230.  Lateral   Pressure. — We  have  already  seen 
that  downward  and  upward  pressure  are  proportional  to 
the  depth  of  the  liquid.     Owing  to  the  principle  of  equal 
transmission  of  pressure  in  all  directions,  the  same  holds 

true  for  lateral  pressure,  the 
effects  of  which  are  some- 
times disastrously  shown  by 
the  giving  way  of  flood-gates, 
dams,  and  reservoirs. 

(a.)  These  effects  of  lateral 
pressure  may  be  safely  illus- 
trated by  a  tall  vessel  provided 
with  a  stop-cock  near  its  base, 
and  arranged  to  float  upon  the 
water.  When  this  vessel  is  filled 
with  water,  the  lateral  pressure 
at  any  two  points  at  the  same 
depth  and  opposite  each  other 
FIG.  76.  will  be  equal.  Being  equal  and 

opposite  they  will  neutralize  each  other  and  produce  no  motion.  If 
now  the  stop-cock  be  opened,  the  pressure  at  that  point  tending  to 
drive  the  apparatus  in  a  certain  direction,  say  toward  the  left,  is  re- 
moved ;  the  pressure  at  the  opposite  point  tending  to  drive  the 
vessel  toward  the  right,  being  no  longer  opposed  by  its  equal,  will 
now  produce  motion  and  the  vessel  will  float  in  a  direction  opposite 
to  that  of  the  spouting  water.  Instead  of  being  floated  upon  water, 
the  vessel  may  be  supported  by  a  long  thread.  The  same  principle 
is  illustrated  in  Barker's  Mill.  (Fig.  91.) 

231.  Rule  for  Lateral  Pressure. — To  find  the 
pressure  upon  any  vertical  surface,  find  the  weight 
of  an  imaginary  column  of  the  liquid  whose  base 
is  equal  to  the  given  surface  and  whose  altitude 
is  the  same  as  the  depth  of  the  centre  of  the  given 
surface  Tjelow  the  surface  of  the  liquid. 


HYDROSTATICS.  127 


EXERCISES. 

1.  What  will  be  the  pressure  on  a  dam  in  20  feet  of  water,  the 
dam  being  30  feet  long  ? 

2.  What  will  be  the  pressure  on  a  dam  in  6  m.  of  water,  the  dam 
being  10  m.  long  ? 

3.  Find  the  pressure  on  one  side  of  a  cistern  5  feet  square  and  12 
feet  high,  filled  with  water. 

4.  Find  the  pressure  on  one  side  of  a  cistern  2  m.  square  and  4  m. 
high,  filled  with  water. 

5.  A  cylindrical  vessel  having  a  base  of  a  sq.  yd. ,  is  filled  with 
water  to  the  depth  of  two  yards.     What  pressure  is  exerted  upon 
the  base? 

6.  A  cylindrical  vessel  having  a  base  of  a  sq.  m.  is  filled  with  water 
to  the  depth  of  two  meters.     What  pressure  is  exerted  upon  the 
base? 

7.  What  will  be  the  upward  pressure  upon  a  horizontal  plate  a 
foot  square  at  a  depth  of  25  ft.  of  water  ? 

8.  What  will  be  the  upward  pressure  upon  a  horizontal  plate  SO 
cm.  square  at  the  depth  of  8  m.  of  water  ? 

9.  A  square  board  with  a  surface  of  9  square  feet  is  pressed 
against  the  bottom  of  the  vertical  wall  of  a  cistern  in  which  the 
water  is  8|  feet  deep.    What  pressure  does  the  water  exert  upon 
the  board  ? 

10.  A  cubical  vessel  with  a  capacity  of  1728  cubic  inches  is  two- 
thirds  full  of  sulphuric  acid,  which  is  1.8  times  as  heavy  as  water. 
Find  the  pressure  on  one  side. 

11.  A  conical  vessel  has  a  base  with  an  area  of  237  sq.  cm.     Its 
altitude  is  38  cm.     It  is  filled  with  water  to  the  height  of  35  cm. 
Find  the  pressure  on  the  bottom.  Ans.  8295  g. 

12.  In  the  above  problem,  substitute  inches  for  centimeters,  and 
then  find  the  pressure  on  the  bottom. 

13.  What  would  be  the  total  liquid  pressure  on  a  prismatic  vessel 
containing  a  cubic  yard  of  water,  the  bottom  of  the  vessel  being  2 
by  3  feet  ? 

14.  The  lever  of  a  hydrostatic  press  is  6  feet  long,  the  piston-rod 
being  1  foot  from  the  fulcrum.     The  area  of  the  tube  is  one-half 
square  inch  ;  that  of  the  cylinder  is  100  square  inches.     Find  the 
weight  that  may  be  raised  by  a  power  of  75  Ibs. 

15.  What  is  the  pressure  on  the  bottom  of  a  pyramidal  vessel 
filled  with  water,  the  base  being  2  by  3  feet,  and  the  height,  5  feet? 

16.  What  is  the  pressure  on  the  bottom  of  a  conical  vessel  4  feet 
high  filled  with  water,  the  base  being  20  inches  in  diameter  ? 


128  EQUILIBRIUM. 

Recapitulation. — In  this  section  we  have  considered 
Ineompressibility ;  the  Transmission  of  Pres- 
sure with  Explanation  and  Illustration  ;  Pas- 
cal's Law  with  Argument  and  Conclusion 
therefrom;  one  of  Pascal's  Experiments ;  the 
Hydrostatic  Bellows;  the  Hydrostatic  Press; 
Downward  Pressure  with  experimental  illustra- 
tions; Rule  for  computing  downward  pressure ;  Up- 
ward Pressure  with  experimental  illustrations; 
Rule  for  computing  upward  pressure ;  Lateral 
Pressure  with  experimental  illustrations;  Rule  for 
computing  lateral,  pressure. 


j@aEC.Ti ON  H. 

»A: 
EQUILIBRIUM.— CAPILLARITY.— BOUYANCY. 

232.  Conditions   of  Liquid  Rest.— The   force 
of  gravity  tends  to  draw  all  liquid  particles  as  near  the 
earth's  centre  as  possible.    The  following  are  necessary 
conditions,  that  a  liquid  may  be  at  rest : 

(1.)  The  free  surface  of  the  liquid  must  be 
everywhere  perpendicular  to  the  force  of  gravity, 
i.  e.,  horizontal.  In  the  case  of  the  ocean,  this  condition 
is  modified  by  the  so-called  centrifugal  force,  which  gives 
rise  to  the  spheroidal  shape  of  the  earth. 

(2.)  Every  molecule  must  be  subjected  to  equal 
and  contrary  pressures  in  every  direction. 

233.  Equilibrium    of    Liquids.— A    liquid   of 
small  surface  area  is  said  to  be  level  when  all  the  points  of 


EQUILIBRIUM. 

its  surface  are  in  the  same  horizontal  plane, 
idea  is  expressed  in  the 
familiar  saying,  water 
seeks  its  level.  This 
is  true  whether  the 
liquid  be  placed  in  a 
single  vessel  or  in  sev- 
eral vessels  that  com- 
municate with  each 
other. 


234.  Communi- 
cating   Vessels. — 

When    any    liquid    is 
placed  in  one  or  more 


EBSITY 

The  central 


FIG.  77. 


of  several  vessels  communicating  with  each  other,  it  will 
not  come  to  rest  until  it  stands  at  the  same  height 
in  all  of  the  vessels,  so  that  all  of  the  free  surfaces  lie 
in  the  same  horizontal  plane.  This  principle  is  prettily 
illustrated  by  the  apparatus  represented  in  Fig.  77.  It 
consists  of  such  communicating  vessels  containing  a  liquid. 

(a.)  This  important  principle  that  "  water  seeks  its  level"  finds  a 
gigantic  illustration  in  the  system  of  water-pipes  by  which  water  is 
distributed  in  cities  and  large  towns.  Brought  or  pumped  into  an 
elevated  reservoir  near  the  city,  the  water  flows,  in  obedience  to  the 
force  of  gravity,  through  all  the  turns  and  windings  of  all  the  pipes 
connected  with  the  reservoir,  and  is  thus  brought  into  thousands  of 
buildings.  Into  any  of  the  rooms  of  any  of  these  houses  the  water 
may  thus  be  led,  provided  only  that  the  ends  of  the  pipes  be  below 
the  level  of  the  water  in  the  reservoir. 

(&.)  Among  the  many  other  results  of  this  tendency  of  water  to 
seek  its  level  may  be  mentioned  the  action  of  springs  and  Artesian 
wells,  the  use  of  locks  on  canals,  the  spirit-level,  the  flow  of 
streams,  etc. 


130 


CAPILLARITY. 


235.  Capillary  Attraction.  —  The   statements 
made  concerning  the  equilibrium  of  liquids  are  subject  to 
one  important  modification.     When  the  vertical  sides  of 
the  containing  vessel  are  very  near  each  other,  as  in  the 
case  of  small  tubes,  the  force  of  adhesion  manifests  itself 
in  a  way  known  as  capillary  attraction. 

236.  Capillary    Phenomena.— If  a  clean  glass 
rod  be  placed  vertically  in  water,  the  water  will  rise  above 
its  level  at  the  sides  of  the  glass.     If  the  rod  be  now 
plunged  into  mercury,  this  liquid  will  be  depressed  instead 
of  raised.  If  the  experiments  be  repeated,  it  may  be  noticed 
that  the  water  wets  the  glass  while  the  mercury  does  not. 
If  the  glass  be  smeared  with  grease  and  placed  in  water, 
the  surface  of  the  water  will  be  depressed ;  if  a  clean  lead 
or  zinc  plate  be  placed  in  the  mercury  the  surface  of  the 


FIG.  78. 

mercury  will  be  raised.  In  this  case  the  greased  glass  will 
come  out  dry,  no  water  adhering  to  it,  while  mercury  will 
adhere  to  the  lead  or  zinc.  This  is  found  to  be  invariably 
true:  all  liquids  that  will  wet  the  sides  of  solids 
placed  in  them  will  be  lifted,  while  those  that  do 
not  will  be  pushed  down.  In  the  figure,  a  represents 


ARCHIMEDES'   PRINCIPLE.  131 

a  glass  rod  in  water  ;   I,  a  glass  tube  in  water ;   and  c,  a 
glass  tube  in  mercury. 

(a.)  This  form  of  adhesion  is  known  as  capillary  attraction  be- 
cause its  phenomena  are  best  shown  in  tubes  as  fine  as  a  hair  (Latin 
capittus).  If  fine  glass  tubes  be  placed  in  water,  the  liquid  will 
rise,  wet  the  tube,  and  have  a  concave  surface.  If  they  be  placed  in 
mercury,  the  liquid  will  be  depressed,  will  not  wet  the  tube,  and 
will  have  a  convex  surface.  The  finer  the  tube,  the  greater  the 
capillary  ascent  or  depression. 

237.  Displacement  of  a  Fluid  by  an  Im- 
mersed Solid. — A  solid  immersed  in  a  fluid  will 
displace  exactly  Us  own  bulk  of  the  fluid.    This  may 
be  proved,  if  desirable,  by  plunging  a  heavy  body  of  known 
rolume,  as  a  cubic  centimeter  of  iron,  into  water  contained 
in  a  glass  vessel  graduated  to  cubic  centimeters.     The 
water  will  rise  just  as  if  another  cubic  centimeter  of  water 
had  been  added.    Thus,  the  volume  of  any  irregularly 
shaped  body  may  be  found. 

238.  Archimedes'    Principle.— The    loss    of 
weight  of  a  body  immersed  in  a  fluid  equals  the 
weight  of  the  fluid  ivhich  it  displaces. 

(a.)  It  is  a  familiar  fact  that  a  person  may  easily  raise  to  the  sur- 
face of  the  water  a  stone  which  he  cannot  lift  any  further.  When 
an  arm  or  leg  is  lifted  out  of  the  water  of  a  bath-tub,  there  is  a 
sudden  and  very  perceptible  increase  of  weight  at  the  surface.  Let 
us  try  to  find  a  reason  for  these  familiar  truths.  Imagine  a  cube, 
six  centimeters  on  a  side,  immersed  in  water  so 
that  four  of  its  surfaces  are  vertical  and  its 
upper  horizontal  surface  twelve  centimeters 
below  the  surface  of  the  water.  The  lateral 
pressures  which  the  water  exerts  upon  any  two 
opposite  vertical  surfaces  are  clearly  equal  and 
opposite.  They  will  have  no  tendency  to  move 
the  body.  But  the  vertical  pressures  upon  the 
two  horizontal  surfaces  are  not  equal.  The 
lower  face  will  be  pressed  upward  with  a  force 
represented  by  the  weight  of  (6  x  6  x  18  =)  FIG.  79. 


132  ARCHIMEDES'   PRINCIPLE. 

648  cu.  cm.  of  water  (see  §  228)  while  the  upper  face  will  be  pressed 
downward  with  a  force  represented  by  the  weight  of  (6  x  6  x  12  =) 
432  cu.  cm.  of  water.  The  resultant  of  all  these  forces,  therefore, 
will  be  an  upward  pressure  represented  by  the  weight  of  (648  -432=) 
216  cu.  cm.  of  water.  But  216  cu.  cm.  is  the  volume  of  the  cube,, 
This  upward  pressure  or  buoyant  effort  is  exerted  against  the  force  of 
gravity,  and  diminishes  the  weight  of  the  cube. 

239.  An    Experimental    Demonstration. — 

This  principle  of  Archimedes  may  be  experimentally  veri- 
fied as  follows :  From  one  end  of  a  scale-beam  suspend  a 


FIG.  80. 

cylindrical  bucket  of  metal,  I,  and  below  that  a  solid  cyl- 
inder, a,  which  accurately  fits  into  the  bucket.  Counter- 
poise with  weights  in  the  opposite  scale-pan.  Imjnerse  a 
in  water  and  the  counterpoise  will  descend,  showing  that  a 
has  lost  some  of  its  weight.  Carefully  fill  b  with  water. 
It  will  hold  exactly  the  quantity  displaced  by  a.  Equili- 
brium  will  be  restored. 


BUOYANCY.  133 

(a.)  Insert  a  short  spout  in  the  side  of  a  vessel  (as  a  tin  fruit-can) 
about  an  inch  below  the  top.  Fill  the  vessel  with  water  and  let  all 
above  the  level  of  the  spout  escape.  This  is  to  replace  the  vessel 
of  water  in  which  a  (Fig.  80)  is  immersed.  Instead  of  the  bucket, 
6,  use  a  cup  placed  on  the  scale  pan.  Instead  of  a,  use  any  con- 
venient solid  heavier  than  water,  as  the  fragment  of  a  stone.  Coun- 
terpoise the  cup  and  stone  in  the  air.  Immerse  the  stone  in  the 
water  and  catch,  in  any  convenient  vessel,  every  drop  of  water  that 
overflows.  This  will  be  the  fluid  that  the  solid  displaces.  The 
equilibrium  is  destroyed,  but  may  be  restored  by  pouring  the 
water  just  caught  into  the  cup  on  the  scale-pan. 

24O.  Floating  Bodies.— When  solids  of  different 
densities  are  thrown  into  a  given  liquid,  those  having  den- 
sities greater  than  that  of  the  liquid 
will  sink,  because  the  force  of  gravity 
overcomes  the  buoyancy  of  the  liquid  ; 
those  having  densities  equal  to  that  of 
the  liquid  will  remain  at  rest  in  any 
position  in  the  liquid,  because  the  op- 
posing forces,  gravity  and  buoyancy, 
are  equal;  those  having  densities  less  FIG.  81. 

than  that  of  the  liquid  will  float,  because  the  force  of 
gravity  will  draw  them  down  into  the  liquid  until  they 
displace  enough  of  the  liquid  to  render  the  buoyant  effect 
equal  to  the  weight.  Hence,  a  floating  body  displaces 
Us  own  weight  of  the  fluid.  This  may  be  shown  ex- 
perimentally by  filling  a  vase  with  water.  When  a  float- 
ing body  is  placed  on  the  surface,  the  water  displaced  will 
overflow  and  may  be  caught.  The  water  thus  caught  will 
weigh  the  same  as  the  floating  body. 

(a.)  Place  the  tin  vessel  with  a  spout,  mentioned  in  the  last 
article,  upon  one  scale-pan,  and  fill  it  with  water,  some  of  which 
will  overflow  through  the  spout.  When  the  spout  has  ceased 
dripping,  counterpoise  the  vessel  of  water  with  weights  in  the 
other  scale-pan.  Place  a  floating  body  on  the  water.  This  will 


134  BUOYANCY. 

destroy  the  equilibrium,  but  water  will  overflow  through  the  spout 
until  the  equilibrium  is  restored.  This  shows  that  the  floating 
body  has  displaced  its  own  weight  of  water. 

EXERCISES. 

1.  How  much  weight  will  a  cu.  dm.  of  iron  lose  when  placed  in 
water  ? 

2.  How  much  weight  would  it  lose  in  a  liquid  13.6  times  as  heavy 
as  water  ? 

3.  If  the  cu.  dm.  of  iron  weighs  only  7780  g.,  what  does  your 
answer  to  the  3d  problem  signify  ? 

4.  How  much  weight  would  a  cubic  foot  of  stone  lose  in  water  ? 

5.  If  100  cu.  cm.  of  lead  weigh  1135  g.t  what  will  it  weigh  in 
water  ? 

6.  If  a  brass  ball  weigh  83.8  g.  in  air  and  73.8  g.  in  water,  what  is 
its  volume  ? 

7.  If  a  brass  ball  weigh  83.8  oz.  in  air  and  73.8  oz.  in  water,  what 
is  its  volume  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Conditions  of  Liquids  at  Rest ;  the  Equi- 
librium of  liquids  in  Single  and  Communica- 
ting Vessels ;  the  Water  Supply  of  cities ;  the 
Equilibrium  of  Different  Liquids  in  commu- 
nicating vessels ;  Capillary  Attraction  and  some 
of  its  Phenomena  ;  Capillary  Tubes ;  the 
quantity  of  a  Fluid  Displaced  by  an  immersed 
solid;  the  Buoyancy  of  Fluids  ;  Archimedes' 
Principle  ;  several  Explanations  of  Archimedes' 
Principle  and  its  Experimental  Verification ; 
Floating  Bodies. 


SPECIFIC    GRA  VITY.  135 

ECTION  HI, 


SPECIFIC    GRAVITY. 

241.  What  is  Specific  Gravity  ?— ^e  specific 
gravity  of  a  body  is  the  ratio  between  its  weight 
and  the  weight  of  a  like  volume  of  some  other 
substance  taken  as  a  standard. 

212.    Standard    of    Specific    Gravity.— The 

standard  taken  must  be  invariable.  For  solids  and  liquids, 
the  standard  adopted  is  distilled  water  at  a  tem- 
perature of  4°  C.,  or  39.2°  F.  For  aeriform  bodies,  the 
standard  is  air  or  hydrogen. 

(a.)  The  water  is  to  be  distilled,  or  freed  from  all  foreign  sub- 
stances, because  the  weight  of  a  given  quantity  of  water  varies  with 
the  substances  held  in  solution.  It  is  to  be  at  a  fixed  temperature 
because  of  the  expansion  by  heat.  The  temperature  above  men- 
tioned is  that  of  water  at  its  greatest  density.  In  cases  where  air  or 
hydrogen  is  taken  as  a  standard,  the  additional  condition  of  atmos- 
pheric pressure  must,  for  obvious  reasons,  be  recognized.  The  pres- 
sure to  which  all  observations  in  this  country  are  reduced  is  that 
recorded  by  30  inches  (760  mm.)  of  the  barometer. 

243.  Elements  of  the  Problem. — For  solids 
or  liquids,  the  dividend  is  the  weight  of  the  given 
body ;  the  divisor  is  the  weight  of  the  same  bulk 
of  water ;  the  quotient,  which  is  an  abstract  number,  is 
the  specific  gravity,  and  signifies  that  the  given  body  is  so 
many  times  heavier  than  the  standard.  The  weight  of  the 
same  bulk  of  water  is  found  sometimes  in  one  way  and 
sometimes  in  another,  but  in  every  case  it  is  the  divisor. 
By  grasping  and  keeping  this  idea,  you  will  avoid  much 
possible  confusion.  Of  course,  when  any  two  of  these 
three  are  given,  the  third  can  be  found. 


136 


SPECIFIC  GRAVITY. 


244.  To  Find  the  Specific  Gravity  of  Solids, 

— The  most  common  method  of  finding  the  specific  grav- 
ity of  a  solid  heavier  than  water,  is  to  find  the  weight  of 
the  body  in  the  air  (=:  W),  then  suspend  the  body  by  a 
light  thread  and  find  its  weight  in  water  (—  W),  and 
divide  the  weight  of  the  body  in  air  by  the  weight  of  the 
same  bulk  of  water  (§  238,  Archimedes'  Principle). 

W 
Sp.Gr.=  w-_rw,. 

(a.)  The  method  is  illustrated  by  the  following  example  : 
Weight  of  substance  in  air          =  58|  oz. 
Weight  of  substance  in  water     =  51    oz. 
Weight  of  equal  bulk  of  water  =    7£  oz. 
Specific  gravity  =  58|  oz.  -5-  7J  oz.  =  7.8,  Ans. 


245.  To  Find  the  Specific  Gravity  of  Solids 
Lighter  than  Water.— If  the  given  body  be  lighter 
than  water,  fasten  to  it  some  body  heavy  enough  to  sink 


SPECIFIC  GRAVITY.  137 

it.  Find  the  loss  in  weight  of  the  combined  mass  when 
weighed  in  water.  Do  the  same  for  the  heavy  body. 
Subtract  the  loss  of  the  heavy  body  from  the  loss  of  the 
combined  body.  Divide  the  weight  of  the  given  body  by 
this  difference.  (Show  that  this  divisor  is  as  indicated  in 
§  243.)  A  modification  of  this  method  is  to  balance  the 
sinker  in  water.  Then  attach  to  it  the  light  substance  in 
question,  e .  #.,  a  cork,  and  determine  the  buoyant  effort  of  the 
cork,  /.  e.,  the  weight  of  its  bulk  of  water.  Divide  as  before. 

(a.)  The  first  method  is  illustrated  by  the  following  example : 
(1.)  Weight  of  cork  and  iron  in  air ...   82.4  g. 


(2.) 
(3.) 
(4.) 
(5.) 
(6.) 
(7.) 
(8.) 


water 52.4  g. 

water  displaced  by  cork  and  iron  —  30.    g. 

iron  in  air 77.8  g. 

"       water 67.8  g. 

water  displaced  by  iron 10.    g. 

cork  (3) -(6).... 20.    g. 
cork  in  air (1)  —  (4). .    .  4.6  g. 


(9.)  Spec  fie  gravity  of  the  cork (8)  -s-  (7) 23 

(10.)  "        "       iron (4)  -f-  (6) 7.78 

246.  To    Find    the     Specific    Gravity    of 
Liquids. — The    principle    is    unchanged.      A    simple 
method  is  as  follows :    Weigh  a  flask  first  empty  ;   next, 
full  of  water  ;  then,  full  of  the  given  liquid.     Subtract  the 
weight  of  the  empty  flask  from  the  other  two  weights ; 
the  results  represent  the  weights  of  equal  volumes  of  the 
given  substance  and  of  the  standard.    Divide  as  before. 
A  flask  of  known  weight,  graduated  to  measure  100  or 
1000  grams  or  grains  of  water  is  called  a  specific  gravity 
flask.    Its  use  avoids  the  first  and  second  weighings  above 
mentioned,  and  simplifies  the  work  of  division. 

247.  Another  Simple  Method.-The  specific  gravity  of 
a  liquid  may  be  easily  determined  as  follows  :    Find  the  loss  of 
weight  of  any  insoluble  solid  in  water  and  in  the  given  liquid. 


138  SPECIFIC  GRAVITY. 

From  §  238,  determine  what  these  two  losses  represent.  Divide  as 
before.  The  solid  used  is  called  a  specific  gravity  bulb. 

Other  methods  are  sometimes  used,  but  as  they  depend  upon  the 
principles  already  explained,  they  need  not  be  set  forth  here. 
Some  of  them  will  be  illustrated  in  the  problems. 

248.  To  Find  the  Specific  Gravity  of  Gases. 

—The  specific  gravity  of  an  aeriform  body  is  always  found 
by  comparing  the  weight  of  equal  volumes  of  the  standard 
(air  or  hydrogen)  and  of  the  given  substance.  The  method 
is  strictly  analogous  to. the  one  first  given  for  liquids.  The 
air  is  removed  from  the  flask  with  an  air-pump — an  in- 
strument to  be  studied  soon.  The  accurate  determination 
of  the  specific  gravity  of  gases  presents  many  practical  dif- 
ficulties which  cannot  be  considered  in  this  place. 

Note. — The  weight  of  any  solid  or  liquid  (in  grams  per  cu.  cm.) 
represents  its  specific  gravity.  Bodies  are  commonly  weighed  in 
the  air.  But,  in  common  with  all  other  fluid  bodies,  the  air  has 
weight  and  therefore  (§  238)  diminishes  the  true  weight  of  all  bodies 
thus  weighed.  This  diminution  is  generally  disregarded,  but  in 
certain  delicate  operations  it  must  be  carefully  considered. 

249.  Hydrometers. — Instruments,  called  hydrom- 
eters or  areometers,  are  made  for  the  more  convenient  de- 
termination of  specific  gravity.    They  dispense  with  the 
use  of  the  balance,  an  instrument  requiring  careful  hand- 
ling and  preservation.    Hydrometers  are  of  two  kinds : 
(1.)  Hydrometers  of  constant  volume,  as  Nicholson's. 
(2.)  Hydrometers  of  constant  weight,  as  Beaume's. 

250.  Nicholson's     Hydrometer.—  Nicholson's 
hydrometer  is  a  hollow  cylinder  carrying  at  its  lower  end 
a  basket  d,  heavy  enough  to  keep  the  apparatus  upright 
when  floated  on  water.     At  the  top  of  the  cylinder  is  a 
vertical  rod  carrying  a  pan  a,  for  holding  weights,  etc. 
The  whole  apparatus  must  be  lighter  than  water,  so  that  a 
certain  weight  (=  W,)  must  be  put  into  the  pan  to  sink 


SPECIFIC   GRAVITY. 


139 


FIG.  83. 

the  apparatus  to  a  fixed  point  marked  on  the  rod  (as  c). 
The  given  body,  which  must  weigh  less  than  W,  is  placed 
in  the  pan,  and  enough  weights  (=  w)  added  to  sink  the 
point  c  to  the  water  line.  It  is  evident  that  the  weight  of 
the  given  body  is  W  —  w.  It  is  now  taken  from  the  pan 
and  placed  in  the  basket,  when  additional  weights  (=  x) 
must  be  added  to  sink  the  point  c  to  the  water  line. 

W—w 


Sp.  Gr.  = 


x 


(Why  ? 


251.  Fahrenheit's  Hy- 
drometer. — Fahrenheit's  Hy- 
drometer is  similar  in  form  to 
Nicholson's,  but  is  made  of  glass 
instead  of  metal,  so  that  it  may 
be  used  in  any  liquid.  The  bas- 
ket is  replaced  by  a  bulb  loaded 
with  shot  or  mercury.  The 
weight  of  the  instrument  (—  W) 
is  accurately  determined.  The  H 
instrument  is  placed  in  water, 


FIG.  84. 


140 


SPECIFIC   GRA  VITY. 


and  a  weight  (=  w),  sufficient  to  sink  the  point  c  to  the 
water  line,  is  placed  in  the  pan.  The  weight  of  water  dis- 
placed by  the  instrument  =  W  +  w.  The  hydrometer  is 
now  removed,  wiped  dry,  and  placed  in  the  given  liquid. 
A  weight  (=  z),  sufficient  to  sink  the  hydrometer  to  c,  is 
placed  in  the  pan. 


Note.  —  A  Nicholson's  hydrometer  may  be  used  as  a  Fahrenheit's 
in  any  liquid  which  has  no  chemical  action  upon  the  metal  of  which 
it  is  made.  Neither  of  these  hydrometers  gives  results  as  accurate 
as  those  obtained  by  the  methods  previously  given. 

252.    Constant    Weight    .Hydrometers.—  A 

hydrometer  of  constant  weight  consists  of  a  glass  tube  neai 

the  bottom  of  which  are  two  bulbs.    The  lower  and  smaller 

bulb  is  loaded  with   mercury  or  shot. 

The  tube  and  upper  bulb  containing  air, 

the  instrument  is  lighter  than  water. 

The  point  to  which  it  sinks  when  placed 

in  pure  water  is  generally  marked  zero. 

The  tube  is  graduated  above  and  below 

zero,  the   graduation  being  sometimes 

upon  a  piece  of  paper  placed  within  the 

tube.    As  a  long  stem  would  be  incon- 

venient, it  is  customary  to  have  two  in- 

struments,  one  having  zero    near  the 

top,  for  liquids  heavier  than  water;  the 

other  having   zero  near  the  bulb,  for 

liquids  lighter  than  water.     The  scale  of  graduation  is  arbi- 

trary, varying  with  the  purpose  for  which  the  instrument  is 

intended.     These  instruments  are  more  frequently  used  to 

determine  the  degree  of  concentration  or  dilution  of  certain 


FIG.  85. 


SPECIFIC  GRAVITY. 


141 


liquids,  as  acids,  alcohols,  milk,  solutions  of  sugar,  etc., 
than  their  specific  gravities  proper.  According  to  their 
uses  they  are  known  as  acidometers,  alcoholometers,  lac- 
tometers, saccharometers,  etc.  They  all  depend  upon  the 
principle  that  a  floating  body  will  displace  its  own  weight 
of  the  liquid  upon  which  it  floats,  and,  consequently,  a 
greater  volume  of  light  than  of  heavy  liquids. 

253.  Tables  of  Reference*— (1.)  Specific  gravities 
of  some  solids : 


Indium 23.00  j  Brass 8.38 

Platinum 22.069  Iron  (bar) 7.78 

Gold  (forged)...  19. 36  ' 

Lead  (cast) 11.35 

Silver  (cast)....  10. 47 


Marble  (statuary).  2. 83 
Anthracite  Coal.  .1.80 

Tin  (cast) 7.29  '  Bituminous  Coal.  1.25 

Iron  (cast) 7.21  !  Ice  (melting) 92 

Zinc  (cast) 6.86  j  Pine 65 


8.79  I  Flint  Glass 3.33  !  Cork 24 


Copper  (cast). . 

(2.)  Specific  gravities  of  some  liquids: 

Mercury 13.6 

Sulphuric  Acid. .  1.84 
Hydrochloric  Acid  1.24 


Nitric  Acid 1.22 

Milk 1.03 

Sea  Water..    ..1.026 


Turpentine 87 

Alcohol 8 

Ether..  .  .72 


(3.)  Specific  gravities  of  some  gases:    (Barometer  =  760 
mm. ;  Temperature  =  32°  F.  or  0°  C.) 


Am  —  STANDARD. 

Hydroiodic  Acid 4.41 

Carbon  Dioxide 1.52 

Oxygen 1.1 

Air 1.0 

Nitrogen.. 97 

Hydrogen 069 


HYDROGEN  =  STANDARD. 

Hydroiodic  Acid 64 

Carbon  Dioxide 22 

Oxygen 16 

Air 14.5 

Nitrogen 14 

Hydrogen 1 


Note. — The  weight  of  a  cubic  foot  of  any  solid  or  liquid  is  equal 
to  62.421  Ibs.  avoirdupois  multiplied  by  its  specific  gravity. 

The  weight  of  a  cubic  centimeter  of  any  solid  or  liquid  is  equal 
to  1  gram  multiplied  by  its  specific  gravity. 

The  weight  of  a  liter  (or  cu.  dm.)  of  any  solid  or  liquid  is  equal 
to  1  Kg.  multiplied  by  its  specific  gravity. 

The  tables  above  give  only  average  densities.  Any  given  speci- 
men may  vary  from  the  figures  there  given. 


SPECIFIC  GRAVITY. 


EXEKCISES. 

Wote.—Be  on  the  alert  to  recognize  Archimedes'  Principle  in 
disguise.  Consider  the  weight  of  water  62|  Ibs.  per  cubic  foot. 

The  numbers  obtained  for  the  right  hand  column  may  be  either 
plus  or  minus  ;  the  former  sign  denotes  weight  in  the  fluid  ;  the 
latter,  the  load  it  could  support  in  the  fluid. 


No. 

Weight 
in  Air. 

Weight 
in  Water. 

Loss  of 
Weight  in 
Water. 

Spec. 
Grav. 

Volume. 

ANY  FLUID. 

Sp.  Gr.  of 

Weight  in 

1 

1500  Ibs. 

1000  lb". 

I 

>             ?  cu  ft. 

1.5 

? 

2 

500007. 

9 

1500  oz. 

? 

i 

? 

2000  oz. 

3 

? 

1875  g. 

? 

2 

? 

1.8 

9 

4 

? 

9375  g. 

? 

? 

? 

1.5 

4687.5  g. 

5 

? 

? 

? 

7.5 

300  cu.  cm. 

2.5 

? 

6 

? 

1125  Ibs. 

? 

? 

? 

3 

875  Ibs. 

7 

9 

? 

? 

? 

8  cu.  ft. 

13.6 

2700  Ibs. 

8 

? 

? 

? 

6.86 

5  cu.  dm. 

13.6 

? 

9 

IKg. 

? 

? 

1 

? 

? 

200  g. 

10 

? 

? 

? 

2.83 

10  cu.  ft. 

.8 

? 

11.  A  bone  weighs  2.6  ounces  in  water  and  6.6  ounces  in  air; 
what  is  its  specific  gravity  ? 

12.  A  body  weighing  453  g.  weighs  in  water  429.6  g.;  what  is  its 
specific  gravity  ? 

13.  A  piece  of  metal  weighing  52.35  g.  is  placed  in  a  cup  filled 
with  water.     The  overflowing  water  weighed  5  g.     What  was  the 
specific  gravity  of  the  metal  ? 

14.  (a.)  A  solid  weighing  695  g.  loses  in  water  83  g. ;  what  is  its 
specific  gravity  ;  (&)  how  much  would  it  weigh  in  alcohol  of  specific 
gravity  0.792? 

15.  A  1000  grain  bottle  will  hold  708  grains  of  benzoline.     Find 
the  specific  gravity  of  the  benzoline. 

16.  A  solid  which  weighs  2.4554  oz.  in  air,  weighs  only  2.0778  oz. 
in  water.    Find  its  specific  gravity. 

17.  A  specimen  of  gold  which  weighs  4.6764  g.  in  air  loses  0.2447 
g.  weight  when  weighed  in  water.     Find  its  specific  gravity. 

18.  A  ball  weighing  970  grs.,  weighs  in  water  895  grs.,  in  alcohol 
910  grs. ;  find  the  specific  gravity  of  the  alcohol. 

19.  A  body  loses  25  grs.  in  water,  23  grs.  in  oil,  and  19   grs.  in 
alcohol.     Required  the  specific  gravity  of  the  oil  and  the  alcohol. 


SPECIFIC  GRAVITY.  143 

30.  A  body  weighing  1536  g.  weighs  in  water  1283  g.;  what  is  its 
specific  gravity  ? 

21.  Calculate  the  specific  gravity  of  sea  water  from  the  following 

data 

Weight  of  bottle  empty 3.5305  g. 

"      filled  with  distilled  water....  7.6722  g. 

sea  "      ...  7.7849  g. 

22.  Determine  the  specific  gravity  of  a  piece  of  wood  from  the 
following  data :    Weight  of  wood  in  air,  4  g. ;   weight  of  sinker, 
10  g.;  weight  of  wood  and  sinker  under  water  8.5  g.;    specific 
gravity  of  sinker,  10.5. 

23.  A  piece  of  a  certain  metal  weighs  3.7395  g.  in  air  ;   1.5780  g. 
in  water  ;  2.2896  g.  in  another  liquid.     Calculate  the  specific  grav- 
ities of  the  metal  and  of  the  unknown  liquid. 

24.  Find  the  specific  gravity  of  a  piece  of  glass  if  a  fragment  of 
it  weigh  2160  grains  in  air,  and  1511]  grains  in  water. 

25.  A  lump  of  ice  weighing  8  Ibs.  is  fastened  to  16  Ibs.  of  lead. 
In  water  the  lead  alone  weighs  14.6  Ibst  while  the  lead  and  ice  weigh 
13.712  Ibs.     Find  the'specific  gravity  of  the  ice. 

26.  Apiece  of  lead  weighing  600  g.,  weighs  545  g.  in  water  and 
557  g.   in  alcohol,      (a.)  Find  the  sp.   gr.   of  the  lead  ;    (6)  of  the 
alcohol,     (c.)  Find  the  bulk  of  the  lead. 

27.  A  person  can  just  lift  a  300  pound  stone  in  the  water  ;  what 
is  his  lifting  capacity  in  the  air  (specific  gravity  of  stone  =  2.5)  ? 

In  the  next  three  examples,  the  weight  of  the  empty  flask  is  not 
taken  into  account. 

28.  A  liter  flask  holds  870  g.  of  turpentine  ;   required  the  sp.  gr. 
of  the  turpentine. 

29.  A  liter  flask,  containing  675  g.  of  water,  on  having  its  remain- 
ing  space  filled  with  fragments  of  a  mineral,  was  found  to  weigh 
1487.5  g.;  required  the  specific  gravity  of  the  mineral. 

30.  A  liter  flask  was  four-fifths  filled  with  water  ;  the  remaining 
space  being  filled  with  sand  the  weight  was  found  to  be  1350  g. ; 
required  the  specific  gravity  of  the  sand. 

31.  A  weight  of  1000  grs.  will-sink  a  certain  Nicholson's  hydrom- 
eter to  a  mark  on  the  rod  carrying  a  pan.     A  piece  of  brass  plus  40 
grs.  will  sink  it  to  the  same  mark.v  WThen  the  brass  is  taken  from 
the  pan  and  placed  in  the  basket,  it  requires  160  grs.  in  the  pan  to 
sink  the  hydrometer  to  the  same  mark  on  the  rod.     Find  the  specific 
gravity  of  the  brass. 

32.  A  Fahrenheit's  hydrometer,  which  weighs  2000  grs.,  requires 
1000  grs.  in  the  pan  to  sink  it  to  a  certain  depth  in  water.    It  requires 
3400  grs.  in  the  pan  to  sink  it  to  the  same  depth  in  sulphuric  acid. 
Find  the  specific  gravity  of  the  acid. 


144  SPECIFIC  GRAVITY. 

33.  A  certain  body  weighs  just  10  g.    It  is  placed  in  one  of  the 
scale-pans  of  a  balance  together  with  a  flask  full  of  pure  water. 
The  given  body  and  the  filled  flask  are  counterpoised  with  shot  in 
the  other  scale-pan.     The  flask  is  removed,  and  the  given  body 
placed  therein,  thus  displacing  some  of  the  water.     The  flask  being 
still  quite  full  is  carefully  wiped  and  returned  to  the  scale-pan, 
when  it  is  found  that  there  is  not  equilibrium.      To  restore  the 
equilibrium,  it  is  necessary  to  place  2.5  g.  with  the  flask.     Find  the 
specific  gravity  of  the  given  body. 

34.  The  volume  of   the  earth   is   1,062,842,000,000,000  cu.  Km. 
Calculate  its  weight  on  the  supposition  that  its  average  density  is 
5.6604. 

35.  A  bottle  holds  2545  mg.  of  alcohol  (sp.  gr.  =  0.8095);  42740 
mg.  of  mercury  ;  5829  mg.  of  sulphuric  acid.     Calculate  the  specific 
gravities  of  the  mercury  and  of  the  acid. 

36.  A  piece  of  cork  weighing  2.3  g.  was  attached  to  a  piece  of 
iron  weighing  38.9  g.,  both  were  found  to  weigh  in  water  26.2  g.,  the 
iron  alone  weighing  33.9  g.  in  water.     Required  the  specific  gravity 
of  the  cork. 

37.  A  piece  of  wood  weighing  300  grs.  has  tied  to  it  a  piece  of 
lead  weighing  600  grs.;  weighed  together  in  water  they  weigh  472.5 
grs.     The  specific  gravity  of  lead  being  11.35,  (a)  what  does  the  lead 
weigh  in  water  ;  (&)  what  is  the  specific  gravity  of  the  wood? 

38.  Calculate  the  specific  gravity  of  a  mineral  water  from  the 
following  data : 

Weight  of  a  bottle  empty 14.1256  g. 

"       filled  with  distilled  water.  .111. 1370  g. 
"  "         "        "     mineral      "    ..111. 7050  g. 

39.  A  Fahrenheit's  hydrometer  weighs  618  grs.     It  requires  93  grs. 
in  the  pan  to  sink  it  to  a  certain  mark  on  the  stem.    When  wiped 
dry  and  placed  in  olive  oil  it  requires  only  31  grs.  to  sink  it  to  the 
same  mark.     Find  the  specific  gravity  of  the  oil. 

40.  A  platinum  ball  weighs  330  g.  in  air,  315  g.  in  water  and  303  g. 
in  sulphuric  acid.    Find  the  specific  gravities  (a)  of  the  ball ;  (b)  of 
the  acid,     (c.)  What  is  the  volume  of  the  ball  ? 

41.  A  hollow  ball  of  iron  weighs  1  Kg.     What  must  be  its  least 
volume  to  float  on  water  ? 

42.  A  piece  of  cork  weighing  30  g.  in  air,  was  attached  to  10  cu. 
cm.  of  lead.    Loss  of  both  in  water  =  159  g.     Required  the  specific 
gravity  of  the  cork. 

43.  A  body  whose  specific  gravity  =  2.8,  weighs  37  g.    Required 
its  weight  in  water. 


HYDROKINETICS.  145 

44.  What  would  a  cubic  foot  of  coal  (sp.  gr.  =  2.4)  weigh  in  a 
solution  of  potash  (sp.  gr.  =  1.2)  ? 

45.  A  platinum  ball   (sp.  gr.  =  22)  weighing  300  g.  in  air  will 
weigh  how  much  in  mercury  (sp.  gr.  =  13.6)  ? 

46.  500  cu.  cm.  of  iron,  specific  gravity  7.8,  floats  on  mercury ; 
with  what  force  is  it  buoyed  up  ? 

47.  An  areometer  weighing  600  grs.  sinks  in  water  displacing  a 
volume  =  v ;  in  a  certain  acid,  displacing  a  volume  =  T9<r  v  ;  find 
the  specific  gravity  of  the  acid. 

Recapitulation. — In  this  section  we  have  considered 
the  Definition  of  Specific  Gravity  ;  the  Stan- 
dards agreed  upon ;  the  Two  Elements  in  specific 
gravity  problems;  the  Rule  for  finding  the  sp.gr.  of 
Solids  heavier  than  Water  ;  the  same  for  Solids 
lighter  than  "Water  ;  the  same  for  Liquids  ;  the 
same  for  Gases ;  the  construction  and  methods  of 
using  Hydrometers ;  Tables  of  specific  gravities, 
and  some  of  the  uses  that  may  be  made  of  them. 


ECTiON    IV. 


HYDROKI  NETICS. 

254.   Velocity   of    Spouting    Liquids.— If  a 

vessel  having  apertures  in  the  side,  similar  to  the  one 
represented  in  Fig.  86,  be  filled  with  water,  the  liquid  will 
escape  from  each  of  the  apertures,  but  with  different  veloc- 
ities. Were  it  not  for  the  resistance  of  the  air,  friction, 
and  the  effect  of  the  falling  particles,  the  water  issuing  at 
V  would  ascend  to  the  level  of  the  water  in  the  vessel ; 
i.  e.,  the  initial  velocity  of  the  water  at  V  would  carry  it 
through  the  vertical  distance  V7i.  But  when  equal  verti- 
7 


146  HYDROKINETICS. 


FIG.  86. 

cal  distances  are  passed  over,  the  initial  velocity  of  an  ascend- 
ing body  is  the  same  as  the  final  velocity  of  a  falling  body. 
(§  13&)  Hence,  the  velocity  of  the  water  as  it  issues  at  V  ia 
the  same  that  it  would  acquire  in  freely  falling  the  vertical 
distance  h  V.  This  velocity  is  caused  by  lateral  pressure. 
This  lateral  pressure  will  be  the  same  at  P,  which  is  at  the 
same  distance  below  the  level  of  the  liquid.  Therefore,  the 
velocity  at  P  will  equal  the  velocity  at  V.  Hence  the  fol- 
lowing law:  The  velocity  of  a  stream  flowing  from 
an  orifice  is  the  same  as  that  acquired  by  a  "body 
freely  falling  from  a  height  equal  to  the  head  cf 
the  liquid. 

(a.)  The  head  is  the  vertical  distance  from  the  centre  of  the 
orifice  to  the  surface  of  the  liquid. 

(6.)  With  what  velocity  will  water  issue  from  an  orifice  144.72  ft. 
below  the  surface  of  the  liquid  ? 

8  =  &t*  (§  128  [3].) 
144.72  =  16.08**        .'.  9  =  t-. 

3  =  t. 

9  =  fft.  (%  128  [1].) 

«  =  82.16  ft.  x  8  =  96.48  ft.   Am. 


EYDROKINETICS.  14? 

(c.)  In  the  solution  above  we  were  obliged  to  find  the  number  of 
seconds  that  would  be  required  for  a  body  to  fall  a  distance  equal 
to  the  head,  before  we  could  use  the  formula  for  the  velocity.  It  is 
desirable,  if  possible,  to  shorten  this  circuitous  process  from  two 
stages  to  one.  This  we  may  do  as  follows  : 


Substituting  this  value  of  t  in  the  formula,  v  =  gt, 

But  h  (the  head)  =  8.  Substituting  this  value  of  8  in  the  last 
equation,  we  have,  for  the  velocity  of  streams  issuing  from  orifices, 
the  following  formula  : 


v  =      y 

The  value  of  g  being  taken  in  feet,  li  and  v  must  represent  feet 
also. 

(d.)  With  what  velocity  will  water  issue  from  an  orifice  under  a 
head  of  144.72  feet  ? 
0  =  8.02      ft 


u  =  8.02  v/i44T72"=  8.02  x  12.03  =  96,48,  the  number  of  feet. 

255.  Orifice  of  Greatest  Range.—  The  path  of 
a  stream  spouting  in  any  other  than  a  vertical  direction  is 
the  curve  called  a  parabola  (§  135).  The  range  of  such  a 
stream  will  be  the  greatest  when  it  issues  from  an  orifice 
midway  between  the  surface  of  the  liquid  and  the  level  of 
the  place  where  the  stream  strikes.  Streams  flowing  from 
orifices  equidistant  above  and  below  this  orifice  of  greatest 
range  will  have  equal  ranges.  (See  Fig.  86.)  The  range, 
in  any  such  case,  may  be  calculated  by  the  laws  of  pro- 
jectiles. 

.  (a.)  Given  an  aperture  four  feet  below  the  surface  and  20  ft. 
above  the  point  where  the  water  strikes,  to  find  the  range  of  the 
jet 

<o  —  8.02  ^/h  =  8.02  x  2  =  16.04  ft.  per  second. 
8=lfft> 

20  -  16.08*3        /.    t  =  1.11  +  sec. 
Range  =  16.04  ft.  x  1.11  =  17.8044  ft. 


148  HTDROKINETICS. 

256.  Volume  Discharged  under  a  Constant 
Head. — To  find  the  volume  discharged  in  a  given 
tune  under  a  constant  head,  multiply  the  area  of 
the  orifice  by  the  velocity,  and  this  product  by  the 
number  of  seconds. 

(a.)  Suppose  that  as  soon  as  the  water  escapes  it  freezes  and  re- 
tains the  form  and  size  given  it  by  the  aperture.  It  will  then  be 
evident  that  the  water  escaping  in  one  second  will  form  a  prism 
whose  section  will  be  the  area  of  the  orifice  and  whose  length  will  be 
the  same  as  the  velocity  of  the  jet.  The  product  of  these  dimensions 
will  give  the  volume  of  the  imaginary  prism,  one  of  which  is  formed 
every  second.  Care  must  be  had  that  the  velocity  and  the  dimen- 
sions of  the  orifice  are  of  the  same  denomination.  The  theoretical 
result  computed  as  above  directed,  will  exceed  the  amount  actually 
discharged.  Why  ?  (See  Appendix  E.) 

257.  The   Flow  of  Liquids  through  Hori- 
zontal    Pipes. — When  liquids  from  a  reservoir    are 
made  to  flow  through  pipes  of  considerable  length,  the 
discharge  is  far  less  than  that  due  to  the  head. 
This  is  chiefly  owing  to  the  friction  of  the  liquid  particles 
against  the  sides  of  the  pipe.    A  horizontal  inch-pipe  200 
feet  long  will  not  discharge  much,  if  any,  more  than  a 
quarter  as  much  water  as  a  very  short  pipe  of  the  same 
size,  the  head  heing  the  same.     Frequent  and  abrupt 
bends  in  the  pipe  retard  the  flow,  and  must  be  provided  for 
by  an  increase  in  the  size  of  the  pipe,  or  an  increase  of 
pressure. 

258.  The   Flow   of  Rivers.— The  friction  of  a 
stream  against  its  solid  bed  fortunately  retards  the  velocity 
of  the  water.     Otherwise  the  velocity  of   the  current  at 
the  mouth  of  a  river,  whose  head  is  elevated   1000  feet 
above   its   mouth,  would  be  about  170  miles  per  hour. 
Such  a  current  would  be  disastrous  beyond  description- 


H  YDR  OKINETICS. 


149 


The  ordinary  river  current  is  from  three  to  five  miles  per 
hour. 

259.  The    Flow    of 
Liquids  through  Verti- 
cal Pipes.— Liquids  flow  ing 
freely  through  vertical  pipes 
exert  no  lateral  pressure. 
The  liquid   will  not  wholly 
fill  the  tube,  but  will  be  sur- 
rounded by  a  thin  film  of  air. 
These  air    particles  will    be 
dragged  down  by  the  adhe- 
sion   of   the    falling    liquid. 
If  a  small  tube  t  be  inserted 
near  the  top  of  the  vertical 
pipe  a  current  of  air  will  be 
forced  through  it  and  down 
the  pipe.      This  air  current 
may  be    utilized    for    blow- 
pipe    and    other     purposes. 
With  a  long  discharge  pipe, 

the  force  with  which  the  air  is  drawn  through  t 
may  be  used  to  remove  the  air  from  a  vessel,  R.  The 
apparatus  then  becomes  a  Sprengel's  or  Bunsen's 
air-pump.  (§§  290,  291.) 

260.  Water-power. — Water  may  be  used  to  turn  a 
wheel  and  thus  move  machinery  by  its  weight,  the  force  of 
the  current,  or  both.     The  wheels  thus  turned  are  of 
different  kinds;   the  availability  of  any  one  being  deter- 
mined by  the  nature  of  the  water  supply  and  the  work  to 
be  done. 


FIG.  87. 


150 


HYDR  0  KINETICS. 


261.  The    Overshot    Wheel.— In    the   overshot 
wheel  the  water  falls  into  buckets  at  the  top,  and  by  its 

weight,  aided  by  the 
force  of  the  current, 
turns  the  wheel.  As 
the  buckets  are  gra- 
dually inverted,  the 
water  is  emptied, 
and  the  load  thus 
removed  from  the 
other  side  of  the 
wheel.  Such  wheels 
it  require  but  little 
FIG.  88.  water  but  a  great 

fall.    It  is  said  that 

they  have  been  made  nearly  100  feet  in  diameter.     The 
water  is  led  to  the  top  of  the  wheel  by  a  sluice,  GH. 

262.  The  Breast  Wheel.— In  the  breast  wheel, 
the  water  acts  upon 

float  boards  fixed 
perpendicular  to  the 
circumference.  The 
stream  being  received 
at  or  near  the  level 
of  the  axis,  both  the 
weight  of  the  water 
and  the  force  of  the 
current  may  be 


turned  to  account. 


FIG. 


263.   The    Undershot    Wheel.— In   the  under- 
shot  wheel,  the  stream  strikes,  near  the  bottom   of  the 


H  YDR  0  KINETICS. 


151 


FIG.  90. 

264.    The    Reac- 
tion   Wheel.  —  The 

reaction  wheel  is  well 
illustrated  by  Barker's 
Mill,  represented  in  Fig. 
91.  It  consists  essential- 
ly of  a  vertical  tube  con- 
necting with  horizontal 
tubular  arms  at  the  bot- 
tom. The  ends  of  these 
arms  are  bent  in  the 
same  direction,  and  are 
open  at  their  ends.  The 
apparatus  is  supported 
on  a  pivot  so  as  to  move 
freely.  Water  is  poured 
into  the  upper  end  of  the 
vertical  cylinder,  and  es- 
capes through  the  open- 
ings a  and  I,  at  the 


wheel,  against  a  few  float 
boards,  which  are  more  or 
less  submerged,  and  thus 
acts  by  the  force  of  the 
current. 

Note. — In  point  of  efficien- 
cy, these  wheels  rank  in  the 
order  above  given,  utilizing 
from  80  to  25  per  cent,  of  the 
total  energy  of  the  stream. 


FIG.  91. 


bent  ends  of  the  arms.    The  wheel  revolves  in  a  direction 


152  HYDROKINETICS. 

opposite  to  that  of  the  water  jets.    The  principle  involved 
was  explained  in  §  230.      (See  Appendix  F.) 

265.  The  Turbine  Wheel.— The  turbine  wheel,  of 
which  there  are  many  varieties,  is  the  most  effective  water- 
wheel  yet  known,  utilizing,  in  some  cases,  85  per  cent,  of 
the  total  energy  of  the  stream. 


FIG.  92. 

(a.)  Fig.  92  represents  one  form  in  perspective  and  in  horizontal 
section  through  the  centre  of  the  wheel  and  case  complete.  The 
wheel  B  and  the  enclosing  case  D  are  placed  on  the  floor  of  a  pen- 
stock wholly  submerged  in  water,  under  the  pressure  of  a  consid- 
erable head.  The  water  enters,  as  shown  by  the  arrows,  through 
openings  in  I),  which  are  so  constructed  that  it  strikes  the  buckets 
of  B  in  the  direction  of  greatest  efficiency.  After  leaving  the 
buckets,  the  "  dead-water "  escapes  from  the  central  part  of  the 
wheel,  sometimes  by  a  vertical  draft  tube,  best  made  of  boiler-iron. 
The  weight  of  the  water  in  this  tube  increases  the  velocity  with 
which  the  water  strikes  the  buckets.  A  central  shaft,  A,  is  carried 
by  the  wheel  and  communicates  its  motion  to  the  machinery  above. 
The  wheel  itself  rests  upon  a  central  pivot  carried  by  cross-arms 
from  the  bottom  of  the  outer  case.  The  case  D  is  covered  with  a 
top  T,  which  protects  the  wheel  from  the  vertical  pressure  of  the 
water.  The  axis  of  the  wheel  passes  through  the  centre  of  this 
cover.  The  openings  by  which  the  water  passes  to  the  wheel  are 
called  chutes.  Sometimes  a  cylindrical  collar,  (7,  is  placed  between 


HYDROKINETICS.  153 

the  wheel  B  and  the  outer  case  D.  This  collar,  called  a  register 
gate,  may  be  turned  about  its  axis  by  the  action  of  a  pinion,  P, 
upon  teeth  placed  upon  the  circumference  of  C.  By  means  of  the 
register  gate,  the  size  of  the  chute  may  be  reduced  and  the  amount 
of  water  used  thus  diminished.  The  water  passages,  to  and  from 
the  wheel,  should  be  of  such  a  size  that  the  velocity  of  the  water 
running  through  them  shall  not  exceed  one  and  a  half  feet  per 
second. 

266.  Lateral  Pressure  of  Running  Water. 

— If  water  could  flow  through  a  pipe  unimpeded  (v  =  8.02 
V  h)>  there  would  be  no  lateral  pressure.  But  as  the 
velocity  is  lessened  by  friction  and  other  causes,  this  lateral 
pressure  begins  to  be  felt ;  when  the  velocity  is  destroyed, 
lateral  pressure  has  its  full  force  again.  Thus,  a  pipe  is 
less  likely  to  burst  when  carrying  running  water  than  when 
filled  with  water  at  rest. 

267.  Bursting  Pressure.— If  a  current  of  water 
flowing  in  a  pipe  be  suddenly  stopped,  much  of   its  mo- 
mentum will  be  changed  to  lateral  or  bursting  pressure. 
This  takes  place  whenever  the  faucet  of  a  water-pipe  is 
suddenly  closed.    Plumbers  frequently  leave  the  ends  of 
such  pipes  in  a  vertical  position  so  that  a  quantity  of  air 
may  be  confined  between  the  closed  end  of  the  pipe  and 
the  water  below.     This  air  by  its  elasticity  acts  as  a  pad  or 
cushion,  thus  lessening  the  suddenness*  of  the  shock  and 
preventing  accidents. 

(a.)  This  principle  is  practically  applied  in  the  "  hydraulic  ram," 
a  contrivance  by  which  the  impulse  of  running  water  when  sud- 
denly checked  may  be  used  to  raise  a  part  of  the  water  through  a 
vertical  distance  greater  than  the  head. 

EXERCISES. 

1.  A  stream  of  water  issues  from  an  orifice  at  the  bottom  of  a 
vessel  containing  water  169  feet  deep.  Give  the  velocity  of  the 
stream  ? 


154 


H  YDR  0  KINETICS. 


2.  How  much  water  issues  in  one  hour  from  the  orifice  in  the 
bottom  of  a  vessel  in  which  the  water  always  stands  12  feet  high, 
the  orifice  being  T^  of  a  square  inch  ? 

3.  How  much  water  per  hour  will  be  delivered  from  an  orifice  of 
2  inches  area,  25  feet  below  the  surface  of  a  tank  kept  full,  no 
allowance  being  made  for  friction,  etc.? 

4.  From  an  orifice,  water  spouts  with  a  velocity  of  96.24  feet. 
What  is  the  head?  Ans.  144ft. 

5.  An  orifice  is  16-08  feet  above  a  horizontal  floor.     Water  spouts 
to  the  distance  of  80.2  feet.     Required  the  head. 

6.  Determine  the  formula  for  the  velocity  of  spouting  liquids, 
using  meters  instead  of  feet.  Ans.  v  =  4.427  \/h. 

7.  A  stream  of  water  issues  from  an  orifice  under  a  head  of  25 
meters.    Find  the  velocity  of  the  stream. 

8.  How  many  liters  of  water  will  flow  through  an  opening  of  10 
sq.  cm.  in  20  seconds,  the  head  being  kept  at  £6  m.  ?    Ans.  531.24  1. 

9.  How  long  will  it  take  for  442,700  cu.  cm.  of  water  to  escape 
through  a  hole  1  centimeter  square  and  100  meters  below  the  surface 
of  the  liquid  ? 

10.  How  long  will  it  take  to  empty  a  tank  having  a  base  3  m.  by 
4  m.  the  water  being  25  m.  deep,  by  means  of  a  sq.  cm.  hole  in  its 
bottom  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Velocity  of  spouting  liquids;  the  orifice  of  Great- 
est Range  ;  the  method  of  computing  the  Volume 
discharged  by  an  orifice  when  the  Head  is  con- 
stant ;  the  flow  of  liquids  through  Pipes  and  Rivers  ; 
the  uses  of  Water-power ;  the  five  kinds  of  Water- 
wheels  ;  the  Lateral  Pressure  of  running  water ; 
the  Bursting  Pressure  when  the  current  is  suddenly 
stopped. 

REVIEW  QUESTIONS  AND  EXERCISES. 

1.  (a.)  Define  Physics.     (&.)  Define  and  illustrate  four  universal 
properties  of  matter. 

2.  (a.)  What  is  the  difference  between  momentum  and  energy  ? 
(6.)  Find  the  momentum  and  (c.)  kinetic  energy  of  a  15  Ib.  ball 
moving  fifty  feet  per  second. 


REVIEW  QUESTIONS.  155 

3.  (a.)  Give  the  third  law  of  motion  and  illustrate  it.    (6.)  Give 
the  law  of  reflected  motion. 

4.  (a.)  What  would  a  1470  Ib.  ball  weigh  at  10,000  miles  above 
the  earth  ?    (&.)  Give  the  law  that  you  use. 

5.  (a.)  How  far  will  a  body  fall  during  the  fourth  second?    (6.) 
How  far  in  four  seconds  ?    (c.)  What  will  be  its  final  velocity  ? 

6.  The  crank  of  an  endless  screw  whose  threads  are  an  inch  apart 
describes  a  circuit  of  72  inches.     The  screw  acts  on  the  toothed 
edge  of  a  wheel  whose  circumference  is  90  inches  and  that  of  its  axle 
13  inches.     On  the  axle  is  wound  a  cord  which  acts  on  a  set  of  pul- 
leys three  in  each  block,  the  force  of  which  pulleys  is  exerted  on 
the  wheel  of  a  wheel  and  axle,  the  wheel  being  4  feet  and  the  axle 
8  inches  in  diameter.     What  weight  on  the  axle  will  be  lifted  by  a 
power  of  30  Ibs.  at  the  crank,  allowing  for  a  loss  of  one -third  by 
friction  ? 

7.  (a.)  What  is  the  length  of  a  pendulum  making  25  vibrations  a 
minute  ?    (5.)  How  many  vibrations  are  made  per  minute  by  a  pen- 
dulum 25  inches  long? 

8.  (a.)  What  is  a  horse-power  ?    (6.)  A  unit  of  work  ?    (c.)  If  a  two 
horse-power  engine  can  just  throw  1056  Ibs.  of  water  to  the  top  of  a 
steeple  in  2  minutes,  what  is  the  height  of  the  steeple  ? 

9.  (a.)  What  are  the  laws  of  machines?    (&.)  The  facts  concerning 
friction?    (c.)  What  is  a  lever?    (d.)  Figure  a  lever  of  each  kind. 
In  a  lever  of  the  second  kind  the  power  is  4J-,  the  weight  is  40 J,  the 
distance  of  the  power  from  the  weight  is  18  in.     (e.)  What  is  the 
length  of  the  lever  ?    (/.)  What  the  length  of  the  short  arm? 

10.  If  the  diameters  of  the  wheel  and  of  the  axle  of  a  wheel  and 
axle  are  respectively  60  in.  and  6  in.,  and  the  power  is  150  Ibs.,  what 
weight  will  be  sustained  ? 

11.  (a.)  Draw  a  system  of  3  fixed  and  2  movable  pulleys.    (&.)  If 
the  power  be  90  and  the  friction  one-third,  what  weight  can  be 
raised  ? 

12.  (a.)  A  weight  of  12  pounds,  hanging  from  one  end  of  a  five 
foot  lever  considered  as  having  no  weight,  balances  a  weight  of  8 
pounds  at  the  other  end.     Find  how  far  the  fulcrum  ought  to  be 
moved  for  the  weights  to  balance  when  each  is  increased  by  two 
pounds.     (&.)  Give  the  law  for  the  screw  ? 

13.  A  capstan,  14  inches  in  diameter,  has  four  levers  each  7  feet 
long.    At  the  end  of  each  lever  a  man  is  pushing  with  a  force  of 
42  pounds.    What  is  the  effect  produced,  one-fourth  of  the  energy 
expended  being  lost  by  friction  ? 


PNEUMATICS, 


ECTfON  I. 


THE  ATMOSPHERE  AND  ATMOSPHERIC  PRESSURE. 

268.  What  is  Pneumatics  ?— Pneumatics  is 
that  branch  of  Physics  which  treats  of  aeriform 
bodies,  their   mechanical  properties,  and  the   ma- 
chines by  ivhich  they  are  used. 

269.  Tension  of  Gases. — However  small  their 
quantity , gases  always  fill  the  vessels  in  which  they 

are  held-  If  a  bladder  or  India  rub- 
ber bag,  partly  filled  with  air,  and 
having  the  opening  well  closed,  be 
placed  under  the  receiver  of  an  air- 
pump,  the  bladder  or  bag  will  be  fully 
distended,  as  shown  in  the  figure, 
when  the  air  surrounding  the  bladder 

,,  is  pumped  out.     The  flexible  walls 

FIG.  93. 

are  pushed  out  by  the  air  confined 
within.     This  tendency  is  called  elastic  force  or  tension. 

270.  The  Type.— As  water  was,  for  obvious  reasons, 
taken  as  the  type  of  liquids,  so  atmospheric  air  will  be 


ATMOSPHERIC  PRESSURE.  157 

taken  as  tl%e  type  of  aeriform  bodies.  Whatever 
mechanical  properties  are  shown  as  belonging  to  air  may 
be  understood  as  belonging  to  all  gases. 

271.  The  Aerial  Ocean. — Air  is  chiefly  a  mixture 
of  two  gases,  oxygen  and  nitrogen,  in  the  proportions  of 
one  to  four  by  volume.  It  is  believed  that  the  atmosphere 
at  its  upper  limit  presents  a  definite  surface  like  that  of 
the  sea :  that  disturbing  causes  produce  waves  there  just  as 
they  do  on  the  sea,  but  that,  by  reason  of  greater  mobility 
and  other  causes,  the  waves  on  the  surface  of  this  aerial 
ocean  are  much  larger  than  any  ever  seen  on  the  surface 
of  the  liquid  ocean.  The  depth  of  this  aerial  ocean  has 
been  variously  estimated  at  from  fifty  to  two  hundred  miles. 

2*72.  Weight  of  Air.— Being  a  form  of  matter,  air 
has  weight.  This  may  be  shown  by  experiment.  A  hol- 
low globe  of  glass  or  metal,  having  a  capacity  of  several 
liters  and  provided  with  a  stop-cock,  is  carefully  weighed 
on  a  delicate  balance.  The  air  is  then  removed  from  the 
globe  by  an  air-pump,  the  stop-cock  closed,  and  the  empty 
globe  weighed  carefully.  The  second  weight  will  be  less 
than  the  first,  the  difference  between  the  two  being  the 
weight  of  the  air  removed.  Under  ordinary  conditions  a 
cubic  inch  of  air  weighs  about  0.31  grains  ;  a  liter  of  air 
weighs  about  1/293  g.,  being  thus  about  -^  as  heavy  as 
water.  (See  Appendix  G.) 

273.  Atmospheric  Pressure. — Having  weight, 
such  a  quantity  of  air  must  exert  a  great  pressure  upon 
the  surface  -of  the  earth  and  all  bodies  found  there.  This 
atmospheric  pressure  necessarily  decreases  as  we  ascend 
from  the  earth's  surface.  For  any  surface,  at  any  ele- 
vation, the  upward,  downward,  or  lateral  pressure  may  be 


158 


ATMOSPHERIC  PRESSURE. 


computed  in  the  same  way  as  for  liquids  (§§  226,  228  and 
231).  vOwing  to  the  great  compressibility  of  aeriform 
bodies,  the  lower  layers  of  the  atmosphere  are  much  more 
dense  than  the  upper  ones,  but  density  and  pressure  alike 
are  constant  in  value  throughout  any  horizontal  layer. 
The  weight  of  a  column  of  air  one  inch  square  extending 
from  the  sea-level  to  the  upper  limit  of  the  atmosphere  is 
about  fifteen  pounds;  a  similar  column,  a  cm.  square, 
weighs  about  1  Kg.  "We  express  this  by  saying  that  the 
atmospheric  pressure  at  the  sea-level  is  fifteen 
pounds  to  the  square  inch)  or  1  Kg.  to  the  sq.  cm. 
Several  illustrations  of  atmospheric  pressure  will  be  given 
after  we  have  considered  the  air-pump. 

274.  Torricelli's  Experiment.— The  intensity  of 
this  pressure  may  be  measured  as  fol- 
lows:— Take  a  glass  tube  a  yard  long, 
about  a  quarter  of  an  inch  in  internal 
diameter.  Close  one  end  and  fill  the 
tube  with  mercury.  Cover  the  other 
end  with  the  thumb  or  finger  and  in- 
vert the  tube,  placing  the  open  end 
in  a  bath  of  mercury.  Upon  removing 
the  thumb,  the  mercury  will  sink, 
oscillate,  and  finally  come  to  rest  at 
a  height  of  about  30  inches,  or  760 
mm.,  above  the  level  of  the  mercury 
in  the  bath.  This  historical  experi- 
ment was  first  performed  in  1643, 
by  Torricelli,  a  pupil  of  Galileo. 
The  apparatus  used,  when  properly 
graduated,  becomes  a  barometer.  FIG.  94. 


ATMOSPHERIC  PRESSURE.  159 

275.  What  Supports  the  Mercury  Column  ? 

- — To  answer  this  very  important  question,  consider  the 
horizontal  layer  of  mercury  molecules  in  the  tube  at  the 
level  of  the  liquid  in  the  bath.  Under  ordinary  circum- 
stances, they  would  hold  their  position  by  virtue  of  the 
tendency  of  liquids  to  seek  their  level.  But  in  this  case, 
they  hold  it  against  the  downward  pressure  caused  by  the 
weight  of  the  mercury  column  above,  which  is  equivalent 
to  fifteen  pounds  to  the  square  inch.  Being  in  a  condi- 
tion of  equilibrium,  they  must  be  acted  upon  by  an  upward 
pressure  of  fifteen  pounds  to  the  square  inch.  It  is  evident 
that  the  pressure  of  the  mercury  in  the  bath  is  not  able  to 
do  this  work,  its  powers  being  fully  tasked  in  supporting 
the  mercury  in  the  tube  up  to  the  level  of  the  particular 
molecules  now  under  consideration.  This  upward  pres- 
sure then  must  be  due  to  some  force  acting  upon  the  sur- 
face of  the  mercury,  and  transmitted  undiminished  by  that 
liquid.  The  only  force,  thus  acting,  is  atmospheric 
pressure,  which  is  thus  measured.  The  original  column 
of  thirty-six  inches  fell  because  its  weight  was  greater 
than  the  opposing  force.  As  it  fell,  its  weight  diminished, 
continuing  to  do  so  until  an  equality  of  opposing  forces 
produced  equilibrium.  (See  Appendix  H.) 

276*  Pascal's  Experiments. — Pascal  confirmed 
Torricelli's  conclusions  by  varying  the  conditions.  He 
had  tho  experiment  repeated  on  the  top  of  a  mountain  and 
found  that  the  mercury  column  was  three  inches  shorter, 
showing  that  as  the  weight  of  the  atmospheric  column 
diminishes,  the  supported  column  of  mercury  also  dimin- 
ishes. He  then  took  a  tube  forty  feet  long,  closed  at  one 
end.  Having  filled  it  with  water3  he  inverted  it  over  a 


160  ATMOSPHERIC  PRESSURE. 

water  bath.  Tfie  water  in  the  tube  came  to  rest  at 
a  height  of  34  feet.  )  The  water  column  was  13.6  times 
as  high  as  the  mercury  column,  but  as  the  specific  gravity 
of  mercury  is  13.6,  the  weights  of  the  two  columns  were 
equal.  Experiments  with  still  other  liquids  gave  corres- 
ponding results,  all  of  which  strengthened  the  theory  that 
the  supporting  force  is  due  to  the  weight  of  the  atmos- 
phere, and  left  no  doubt  as  to  its  correctness. 

277.  Pressure  Measured  in  Atmospheres.— 

A  gas  or  liquid  which  exerts  a  force  of  fifteen  pounds  upon 
a  square  inch  of  the  restraining  surface  is  said  to  exert  a 
pressure  of  one  atmosphere.  A  pressure  of  60  pounds  to 
the  square  inch,  or  4  Kg.  to  the  sq.  cm.,  would 
be  called  a  pressure  of  four  atmospheres. 

278.  The  Accuracy  of  a  Barom- 
eter.— The  accompanying  figure  represents 
the  simplest  form  of  the  barometer.     The  in- 
strument's accuracy  depends  upon  the  purity 
of  the  mercury,  the  accuracy  of  measuring  the 
vertical  distance  from  the  level  of  the  liquid 
in  the  cistern  to  that  in  the  tube,  and  the 
freedom  of  the  space  at  the  top  of  the  tube 
from  air  and  moisture.     In  delicate  observa- 
tions allowance  must  be  made  for  differences 
of    temperature.      In     technical    language, 
"The    barometric    reading    is  corrected   for 
temperature." 

279.  The  Utility  of  a  Barometer. 

— This  instrument's  efficiency  depends  upon 

the  fact  that  variations  in  atmospheric  pres-       FIG.  95. 


A  TMOSPHERIC  PRESS  USE. 


161 


sure  produce  corresponding  variations  in  the  height  of  the 
barometer  column.  It  is  used  to  determine  the  height  of 
places  above  the  sea-level,  foretell  storms,  etc.  When,  at  a 
given  place,  the  "  barometer  falls,"  a  storm  is  generally 
looked  for.  Sometimes  the  storm  does  not  come,  and 
faith  in  the  accuracy  of  the  instrument  is  shaken.  But,  in 
fact,  the  barometer  did  not  announce  a  coming  storm ;  it 
did  proclaim  a  diminution  of  atmospheric  pres- 
sure from  some  cause  or  other.  Its  declarations  are 
perfectly  reliable ;  inferences  from,  those  declarations  are 
subject  to  possible  error. 

280.  The  Aneroid  Barometer. — This  instrument  consists 

of  a  cylindrical  box  of  metal  with  a  top 
of  thin,  elastic,  corrugated  metal.  The 
air  is  removed  from  the  box.  The  top 
is  pressed  inward  by  an  increased 
atmospheric  pressure  ;  whenever  the 
atmospheric  pressure  diminishes,  it  is 
pressed  outward  by  its  own  elasticity 
aided  by  a  spring  beneath.  These 
movements  of  the  cover  are  transmitted 
and  multiplied  by  a  combination  of 
delicate  levers.  These  levers  act  upon 
an  index  which  is  thus  made  to  move 
over  a  graduated  scale.  Such  barome- 
ters are  much  more  easily  portable 
than  the  mercurial  instruments.  They 
are  made  so  delicate  that  they  show 
a  difference  in  atmospheric  pressure 
when  transferred  from  an  ordinary 
table  to  the  floor.  Their  very  delicacy  involves  the  necessity  for  care- 
ful usage  or  frequent  repairs. 

281.  The    Baroscope.— Air,  having  weight,  has 
buoyant  power.     The  Principle  of  Archimedes  (§  238) 
applies  to  gases  as  well  as  to  liquids.     Prom  this  it  follows 
that  the  weight  of  a  body  in  air  is  not  its  true  weight,  but 
that  it  is  less  than  its  true  weight  by  exactly  the  weight  of 


FIG.  96. 


162 


ATMOSPHERIC  PRESSURE. 


the  air  it  displaces.  This  principle  is  illustrated  by  the 
baroscope,  which  consists  of 
a  scale-beam  supporting  two 
bodies  of  very  unequal  size  (as 
a  hollow  globe  and  a  lead 
ball),  which  balance  one  an- 
other in  the  air.  If  the  appa- 
ratus thus  balanced  in  the  air 
be  placed  under  the  receiver 
of  an  air-pump,  and  the  air 
exhausted,  the  globe  will  de- 
scend, thus  seeming  to  be 
heavier  than  the  lead  ball 
which  previously  balanced  it. 
Is  the  globe  actually  heavier 
than  the  lead,  or  not  ? 


FIG.  97. 


EXERCISES. 

1.  Give  the  pressure  of  the  air  upon  a  man  the  surface  of  whose 
body  is  14^  square  feet. 

2.  A  soap-bubble  has  a  diameter  of  4  inches  ;   give  the  pressure 
of  the  air  upon  it.     (See  Appendix  A). 

3.  What  is  the  weight  of  the  air  in  a  room  30  by  20  by  10  feet  ? 

4.  What  will  be  the  total  pressure  of  the  atmosphere  on  a  deci- 
meter cube  of  wood  when  the  barometer  stands  760  mm.  ? 

5.  How  much  weight  does  a  cubic  foot  of  wood  lose  when  weighed 
in  air  ? 

6.  («.)  What  is  the  pressure  on  the  upper  surface  of  a  Saratoga 
trunk  2£  by  3-^  feet?    (&.)  How  happens  it  that  the  owner  can  open 
the  trunk  ? 

7.  When -the  barometer  stands  at  700  mm.  what  is  the  atmos 
pheric  pressure  per  sq.  cm.  of  surface?  Ans.     1033.6  g. 


Note. — In  round  numbers,  atmospheric  pressure  at  the  seale\el 
is  called  15  Ibs.  to  the  sq.  in.,  or  1  kilogram  to  the  sq.  cm. 


TENSION   OF  GASES.  163 

8.  A  certain  room  is  10  m.  long,  8  m.  wide  and  4  m.  high,    (a.) 
What  weight  of  air  does  it  contain  ?    (&.)  What  is  the  pressure  upon 
its  floor?    (c.)  Upon  its  ceiling?     (d.)  Upon  each  end?    (e.)  Upon 
each  side?    (/.)  What  is  the  total  pressure  upon  the  six  surfaces? 
(g.)  Why  is  not  the  room  torn  to  pieces  ? 

9.  An  empty  toy  balloon  weighs  5  g.     When  filled  with  10  I.  of 
hydrogen,  what  load  can  it  lift  ?   (See  Appendix,  G.) 

Recapitulation. — In  this  section  we  have  considered 
the  definitions  of  Pneumatics  and  Tension  ;  the 
Aerial  Ocean  in  which  we  live ;  the  mechanical 
Properties  of  Air  ;  the  weight  of  air  giving  rise  to 
Atmospheric  Pressure;  a  famous  experiment  by 
Torricelli,and  the  explanation  thereof;'  Pascal's  ex- 
periments and  the  conclusion  they  confirmed  ;  the  Ba- 
rometer ;  the  Aneroid  barometer ;  the  Baro- 
scope. 


ECTfON  II. 


THE  RELATION  OF  TENSION   AND  VOLUME  TO 
PRESSURE. 

282.  Tension  of  Gases.— If  a  glass  flask,  provided 
with  a  stop-cock,  be  closed  under  an  atmospheric  pressure 
which  supports  a  mercury  column  of  30  inches,  the  atmos- 
pheric pressure  from  without  is  exactly  balanced  by  the 
tension  (§  269)  of  the  air  within.  If  it  be  closed  under  a 
barometric  pressure  of  28  inches,  this  equality  of  the  two 
pressures  will  continue.  If  the  flask  be  closed  when  the 
surrounding  air  is  subjected  to  a  pressure  of  two  or  three 
atmospheres,  the  equality  will  still  continue.  In  none  of 
these  cases  will  the  glass  be  subjected  to  any  strain  because 


164 


TENSION  OF  GASES. 


of  the  air  within  or  without.  TJie  tension  of  aeriform 
bodies  supports  the  pressure  exerted  upon  them, 
and  is  equal  to  it. 

283.  Experimental  Illustrations  of  Tension.— (1.)  The 
tension  of  confined  air  is  well  illustrated  by  the  common  pop-gun 
It  is  also  well  illustrated  by  the  common  experiment 
with  bursting  squares.  These  "squares"  are  made 
of  thin  glass,  are  about  two  or  three  inches  on  each 
edge,  and  are  hermetically  sealed  under  the  ordinary 
atmospheric  pressure.  The  tension  of  the  air  within, 
acting  with  equal  intensity  against  the  atmospheric 
pressure  from  without,  the  frail  walls  remain  unin- 
jured. When,  however,  the  "square"  is  placed 
under  the  receiver  of  an  air-pump  and  the  external 
pressure  removed,  the  tension  of  15  pounds  to  the 
square  inch  is  sufficient  to  burst  the  walls  outward. 

(2.)  Half  fill  a  small  bottle  with  water,  close  the  neck  with  a  cork 
through  which  a  small  tube  passes.  The  lower  end 
of  this  tube  should  dip  into  the  liquid ;  the  upper 
end  should  be  drawn  out  to  a  smaller  size.  Apply 
the  lips  to  the  upper  end  of  the  tube,  and  force  air 
into  the  bottle.  Notice,  describe,  and  explain  what 
takes  place. 

(3.)  Place  the  bottle,  arranged  as  above  described, 
under  the  receiver  of  an  air-pump,  and  exhaust  the 
air  from  the  receiver.  Water  will  be  driven  in  a  jet 
from  the  tube.  Explain. 


FIG.  98. 


FIG.  99. 


284.  Mariotte's  Law. — TJie  tempera- 
ture remaining  the  same,  the  volume  of 
a  given  quantity  of  gas  is  inversely  as  the  pres- 
sure it  supports. 

285,— Experimental  Verification  of  Mari- 
otte's Law. — This  law  may  be  experimentally  verified 
with  Mariotte's  tube.  It  consists  of  a  long  glass  tube  bent 
as  shown  in  Fig.  100,  the  long  arm  being  open  and  the 
short  arm  closed.  A  small  quantity  of  mercury  is  poured 
into  the  tube,  so  that  the  two  mercurial  surfaces  are  in  the 


TENSION  OF  OASES. 


165 


L 


FIG.  ico. 

same  horizontal  line.  By  holding  the  tuhe  nearly  level, 
bubbles  of  air  may  be  passed  into  the  short  arm  or  from  it 
until  the  desired  result  is  secured.  The  air  in  the  short 
arm  will  then  be  under  an  ordinary  atmospheric  pressure. 
As  more  mercury  is  poured  into  the  long  arm  the  confined 
air  will  be  compressed. 

(a.)  When  the  vertical  distance  between  the  levels  of  the  mercury 
in  the  two  arms  is  one-third  the  height  of  the  barometric  column 
at  the  time  and  place  of  the  experiment,  the  pressure  upon  the 
confined  aii  will  be  f  atmospheres  ;  the  tension  of  the  confined  air 


166 


TENSION  OF  GASES. 


just  supports  tliis  pressure  and  must  therefore  be  f  atmospheres. 
The  volume  of  the  confined  air  is  only  f  what  it  was  under  a  pres- 
sure of  one  atmosphere.  If  more  mercury  be  poured  into  the  long 
arm"  until  the  vertical  distance  between  the  two  mercurial  surfaces 
is  one-half  the  height  of  the  barometric  column,  the  pressure  and 
tension  will  be  -|  atmospheres  ;  the  volume  of  the  confined  air  will 
be  |  what  it  was  under  a  pressure  of  one  atmosphere.  When  mer- 
cury has  been  poured  into  the  long  arm  until  the  vertical  distance 
CA  is  equal  to  the  height  of  the  barometric  column,  the  pressure 
and  tension  will  be  two  atmospheres,  and  the  volume  of  the  confined 
air  will  be  one-half  what  it  was  under  a  pressure  of  one  atmos- 
phere. The  law  has  been  thus  "  verified  "  up  to  27  atmospheres, 
notwithstanding  which  it  is  not  considered  rigorously  exact.  The 
deviation  from  exactness,  however,  can  be  detected  only  by  meas- 
urement of  great  precision. 

286.  The  Rule  Works  both  Ways.— The  law 
holds  good  for  pressures  of  less  than  one  atmosphere,  for 
rarefied  air  as  well  as  for  compressed 
air.  To  show  that  this  is  true,  nearly 
fill  a  barometer  tube  with  mercury  and 
invert  it  over  a  mercury  bath  held  in  a 
glass  tank  as  shown  in  the  figure. 
Lower  the  tube  into  the  tank  until  the 
mercury  levels  within  the  tube  and 
without  it  are  the  same.  The  air  in  the 
tube  is  confined  under  a  pressure  of  one 
atmosphere.  Note  the  volume  of  air  in 
the  barometer  tube.  Raise  the  tube 
until  this  volume  is  doubled.  The 
vertical  distance  between  the  two  mer- 
curial surfaces  will  be  found  to  be  half 
the  height  of  the  barometric  column. 
The  confined  portion  of  air,  which  is 
now  subjected  to  the  pressure  of  half  an 
FIG.  ioi.  atmosphere,  occupies  twice  the  space  it 


TENSION  OF  GASES.  167 

did  under  a  pressure  of  one  atmosphere.  And  so  on.  It 
may  be  more  convenient  to  have  the  barometer  tube  open 
at  both  ends,  the  upper  end  being  closed  with  the  thumb 
or  finger  before  lifting. 

287.  A  Summing:  Up.— From  the  foregoing  experi- 
ments we  have  a  right  to  conclude  that  the  density  and 
tension  of  a  given  quantity  of  gas  are  directly,  and 
that  its  volume  is  inversely,  as  the  pressure  ex- 
erted upon  it.  Representing  the  volumes  of  the  same 
quantity  of  gas  by  V  and  v,  and  the  corresponding  pres- 
sures and  densities  by  P  and  p,  D  and  d,  our  conclusion 
may  be  algebraically  expressed  as  follows : 

H-  P-       ^L 
v  ~~  P  "  Z>' 

EXERCISES. 

1.  Under  ordinary  conditions,  a  certain  quantity  of  air  measures 
one  liter.     Under  what  conditions  can  it  be  made  to  occupy  («.)  500 
cu.  cm.  ?    (&.)  2000  cu.  cm.  ? 

2.  Under  what  circumstances  would  10  cu.  inches  of  air  at  the 
ordinary  temperature  weigh  31  grains  ? 

3.  Into  what  space  must  we  compress  (a.)  a  liter  of  air  to  double 
its  tension  ?    (6.)  A  liter  of  hydrogen  ? 

4.  A  barometer  standing  at  30  inches  is  placed  in  a  closed  vessel. 
How  much  of  the  air  in  the  vessel  must  be  removed  that  the  mer- 
cury may  fall  to  15  inches  ? 

5.  A  vertical  tube,  closed  at  the  lower  end,  has  at  its  upper  end 
a  frictionless  piston  which  has  an  area  of  one  sq.  inch.     The  weight 
of  this  piston  is  five  pounds,     (a.)  What  is  the  tension  of  the  air 
in  the  tube?     (&.)  If  the  piston  be  loaded  with  a  weight  of  ten 
pounds,  what  will  be  the  tension  ? 

6.  When  the  barometer  stands  at  28^  inches,  the  mercury  is  at 
the  same  level  in  both  arms  of  a  Mariotte's  tube.     The  barometer 
rises  and  the  difference  in  the  two  mercurial  surfaces  of  the  Ma- 
riotte's tube  is  half  an  inch,    (a.)  In  which  arm  is  it  the  higher? 
(6.)  Why? 


168  AIR-PUMP. 

7.  Eight  grains  of  air  are  enclosed  in  a  rigid  vessel  of  such  size 
that  the  tension  is  18^  pounds  per  square  inch.  What  will  be  the 
tension  if  three  more  grains  of  air  be  introduced  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Equality  of  tension  and  pressure,  with  several  Ex- 
perimental Illustrations;  Mariotte's  Law; 
the  Verification  of  that  law  for  Compressed 
and  for  Rarefied  Gases;  a  brief  Conclusion  from 
the  teachings  of  these  experiments. 


XgafcECTION  III, 


AIR-PUMPS.— LIFTING   AND    FORCE-PUMPS.— 
SIPHON. 

288.  The  Air-Pump. — TJie  air-pump  is  an 
instrument  for  removing  air  from  a  closed  vessel. 
The  essential  parts  are  shown  in  section  by  Fig.  102 ;  the 
complete  instrument,  as  made  by  Ritchie,  is  represented 
by  Fig.  103. 

The  closed  vessel  R  is  called  a  receiver.  It  fits  accu- 
rately upon  a  horizontal  plate,  through  the  centre  of  which 
is  an  opening  communicating,  by  means  of  a  bent  tube,  /, 
with  a  cylinder,  C.  An  accurately  fitting  piston  moves  in 
this  cylinder.  At  the  junction  of  the  bent  tube  with  the 
cylinder,  and  in  the  piston,  are  two  valves,  v  and  v'y  open- 
ing from  the  receiver  but  not  toward  it.  The  tension  of 
the  air  in  R,  and  the  pressure  of  the  air  upon  the  valves, 
are  equal.  When  the  piston  is  raised,  v'  closes  and  the 
atmospheric  pressure  is  removed  from  v.  The  tension  of 
the  air  in  R  opens  v.  By  virtue  of  its  power  of  indefinite 


AIR-PUMP. 


160 


FIG.  102. 


FIG.  103. 


OF  THF 

UNIVERSITY 


170  AIR-PUMP. 

expansion,  the  air  which,  at  first,  was  in  R  and  t,  now  fills 
R,  ty  and  C.  When  the  piston  is  pushed  down,  v  closes,  v 
opens,  and  the  air  in  C  escapes  from  the  apparatus. 

(a.}  The  lower  valve  v  is  sometimes  supported,  as  shown  in  Fig 
102,  by  a  metal  rod  which  passes  through  the  piston.  This  rod 
works  tightly  in  the  piston,  and  is  thus  raised  when  the  piston  is 
raised,  and  lowered  when  the  piston  is  lowered.  A  button  near  the 
upper  end  of  this  rod  confines  its  motion  within  very  narrow  limits, 
allows  v  to  be  raised  only  a  little,  and  compels  the  piston,  during 
most  of  the  journeys  to  and  fro,  to  slide  upon  the  rod  instead  of 
carrying  the  rod  with  it. 

289.  Degrees  and  Limits  of  Exhaustion.— 

Suppose  that  the  capacity  of  R  is  four  times  as  great  as 
that  of  C.  (The  capacity  of  t  may  he  disregarded.)  Sup- 
pose that  R  contains  200  parts  of  air  (e.  g.,  200  grains), 
and  6Y,  50  parts.  After  lifting  the  piston  the  first  time, 
there  will  be  160  grains  (=  200  x  f)  of  air  in  R,  and  40 
grains  (200  x  -J-)  in  C.  After  the  second  stroke  there  will 
be  128  grains  [=  1GO  x  f  =  200  x  -fr  x  f  =  200  x  (|)2] 
of  air  in  R,  and  32  grains  in  C.  After  n  upward  strokes, 
200  x  ($•)"  grains  of  air  will  remain  in  the  receiver.  Evi- 
dently, therefore,  ive  never  can,  by  this  means,  re- 
move all  the  air  which  R  contains,  although  we 
might  continually  approach  a  perfect  vacuum,  if  this  were 
the  only  obstacle.  It  requires  an  exceedingly  good  air- 
pump  to  reduce  the  tension  of  the  residual  air  to  -^  inch 
of  mercury.  This  limit  is  due  to  several  causes,  among 
which  may  be  mentioned  the  leakage  at  different  parts  of 
the  apparatus,  the  air  given  out  by  the  oil  used  for  lubri- 
cating the  piston,  and  the  fact  that  there  is  a  space  at  the 
bottom  of  the  cylinder  untraversed  by  the  piston. 

290.  SprengePs  Air-Pump. — This  instrument  is 
used  to  apply  the  principles  set  forth  in  §  259  to  the  ex- 


AIR-PUMP.  171 

haustion  of  small  receivers.  The  liquid  used  is  mercury. 
The  vertical  pipe,  below  the  arm  t  (Fig.  87),  must  be 
longer  than  the  barometer  column  (six  feet  is  a  common 
length),  and  have  a  diameter  of  not  more  than  -fa  inch. 
The  mercury  is  admitted  by  large  drops,  which,  filling 
the  pipe,  act  as  valves  and  in  their  fall  force  out  succes- 
sive quantities  of  air  before  them. 

(a.)  With  such  an  instrument,  it  requires  about  half  an  hour  to 
exhaust  a  half  liter  receiver,  but  the  average  result  attainable  is  a 
tension  of  about  one-millionth  atmosphere  or  0.00003  inch  of  mer- 
cury. By  this  means  a  tension  of  only  T^Tnhnnr  atmosphere  has 
been  secured.  The  mercury  acts  as  a  dry,  frictionless,  perfectly 
fitting,  self-adjusting  piston.  Special  precautions  must  be  taken  to 
make  the  connection  air-tight.  The  only  work  of  the  operator  is  to 
carry  the  mercury  from  the  cistern  at  the  foot  of  the  fall  tube  to 
the  funnel  at  the  top. 

291.  Bimsen's    Air-Pump.— In    Bunsen's    air- 
pump  the  principle  is  the  same,  but  the  liquid -used  is 
water,  and  the  length  of  the  vertical  pipe  at  least  thirty- 
four  feet.    Such  an  air-pump  may  be  easily  provided  in  a 
laboratory  where  the  waste-pipe  of  the  sink  has  the  neces- 
sary vertical  height.    The  tube  t  (see  Fig.  87)  being  con- 
nected with  the  receiver,  has  its  free  end  inserted  in  the 
waste-pipe  a  little  way  below  the  sink.    A  stream  of  water 
properly  regulated,  flowing  into  the  sink,  completes  the 
apparatus. 

292.  The    Condenser. — Tlie  condenser  is  an 
instrument  for  compressing  a  large  amount  of  air 
into    a   closed   vessel.      It  differs  from  the  air-pump, 
chiefly,  in  that  its  valves  open  toward  the  receiver. 
The  cylinder  is  generally  attached  directly  to  the  stop- 
cock of  the  receiver.     Its  operation  will  be  readily  un- 
derstood.     Sometimes    the  upper  valve,  vf,   instead  of 


AIR-PUMP. 


being  placed  in  the  piston,  is  placed  in 
a  tube  opening  from  the  side  of  the  cylin- 
der below  the  piston.  By  connecting 
this  lateral  tube  with  a  reservoir  contain- 
ing any  gas,  the  gas  may  be  drawn  from 
the  reservoir  and  forced  into  the  receiver. 
When  thus  made  and  used,  the  instru- 
ment is  called  a  transferrer  (Fig.  104). 

Note. — The  pupil  will  notice  that  in  the  case 
of  the  air-pump,  the  condenser,  the  transferrer, 
and  the  lifting  and  force  pumps  to  be  subse- 
quently considered,  the  valves  open  in  the  di- 
rection in  which  the  fluid  is  to  move. 


FIG.  104.  293.    Experiments.  —  A   person 

having  an  air-pump  has  the  means  of 
performing  almost  numberless  experiments,  some  amusing 
and  all  instructive.  Other  experiments,  which  may  be  per- 
formed without  such  apparatus,  have  been  purposely  de- 
ferred until  now.  The  pupil  should  explain  each  experiment. 

(1.)  The  pressure  of  the  atmosphere,  which  is  transmitted  in  all 
directions,  may  be  illustrated  by  filling  a  tumbler  with  water,  plac- 
ing a  slip  of  thick  paper  over  its  mouth  and  holding  it  there  while 
the  tumbler  is  inverted ;  the  water  will  be  supported  when  the 
hand  is  removed  from  the  card. 

(2.)  Plunge  a  small  tube,  or  a  tube  having  a  small  opening  at  the 
lower  end,  into  water,  cover  the  upper  end  with  the  finger  and  lift 
it  from  its  bath.  The  water  is  kept  in  the  tube  by  atmospheric 
pressure.  Remove  the  finger,  and  the  downward  pressure  of  the 
atmosphere,  which  was  previously  cut  off,  will  counterbalance  the 
upward  pressure  and  the  water  will  fall  by  its  own  weight.  Such 
A  tube,  called  a  pipette,  is  much  used  for  transferring  small  quanti- 
ties of  liquids  from  one  vessel  to  another.  The  pipette  is  often 
graduated. 

(3.)  The  "Sucker"  consists  of  a  circular  piece  of  thick  leather 
with  a  string  attached  to  its  middle.  Being  soaked  thoroughly  in 
water  it  is  firmly  pressed  upon  a  flat  stone  to  drive  out  all  air  from 
between  the  leather  and  the  stone.  When  the  string  is  pulled 


AIR-PUMP. 


173 


FIG.  105. 


gently  there  is  a  tendency  toward  the  formation  of  a  vacuum  be- 
tween the  leather  and  the  stone.  The  stone  is 
now  pushed  upward  with  a  force  of  15  Ibs.  for 
every  square  inch  of  its  lower  surface  (§  273.)  It 
is  pressed  downward  with  a  force  of  15  Ibs.  upon 
each  square  inch  of  its  upper  surface  not  covered  by 
the  "sucker."  The  downward  atmospheric  pres- 
sure upon  the  leather  is  sustained  by  the  string. 
This  difference  between  the  upward  and  down- 
ward atmospheric  pressures  upon  the  stone  may  be 
greater  than  the  gravity  of  the  stone.  Then  we 
say  that  the  stone  is  pulled  up  by  the  "sucker;" 
in  reality  the  stone  is  pusJied  up  by  the  air. 

(4.)  The  hand-glass  is  a  receiver  open  at  both 
ends.  The  lower  end  fits  ac- 
curately upon  the  plate  of  the  air-pump.  (It  is 
well  to  smear  the  plate  with  tallow  in  this  and 
similar  experiments.)  The  hand  is  to  be 
placed  over  the  other  end.  When  the  pump  is 
worked,  the  pressure  of  the  atmosphere  is  felt, 
and  the  hand  can  be  removed  only  by  a  con- 
siderable effort.  The  appearance  of  the  palm 
of  the  hand  at  the  end  of  this  experiment  is  due  to  the  tension  of 
the  air  within  the  tissues  of  the  hand. 

(5.)  Repeat  the  experiment  described  in  §  2C9. 
(6.)  Over  the  upper  end  of  a  cylindrical  receiver,  tie  tightly  a  wet 
bladder,  and  allow  it  to  dry.     Then  ex- 
haust the  air.     The  bladder  will  be  forced 
inward,  bursting  with  a  loud  noise. 

(7.)  Replace  the  bladder  with  a  piece  of 
thin  india-rubber  cloth.  Exhaust  the  air. 
The  cloth  will  be  pressed  inward  and  nearly 
cover  the  inner  surface  of  the  receiver. 
The  hand-glass,  used  in  experiment  (4), 
•will  answer  for  the  two  experiments  last 
given,  by  placing  the  small  end  upon  the 
pump-plate. 

(8.)  Review  the  experiments  mentioned 
in  §  283. 

(9.)  The"  fountain  in  vacua"  consists  of 

a  glass  vessel  through  the  base  of  which  passes  a  tube  terminating 
in  a  jet  within,  and  provided  with  a  stop-cock  and  screw  without. 
By  means  of  the  screw  it  may  be  attached  to  the  air-pump  and  the 


FIG.  107. 


174 


AIR-PUMP, 


FIG.  108. 


FIG.  109. 


air  exhausted.     Remove  the  air,  close  the 

stop  cock,  place  the  lower  end  of  the  tube 

in  water,  open  the  stop -cock  ;  a  beautiful 

fountain  will  be  produced  (Fig.  109). 
(10.)    The   mercury   shower   apparatus 

consists  of  a  cup  through  the  bottom  of 

which  passes  a  plug  of  oak  or  other  porous 
wood.  Place  the  cup  upon 
the  Mnd-glass  with  a  tum- 
bler below ;  pour  some 
mercury  into  the  cup  ;  ex- 
haust the  air,  and  the  at- 
mospheric pressure  will 
force  the  mercury  through 
the  pores  of  the  wood. 

(11.)     The    weight-lifter 
(Fig.  110)  is  an  apparatus 

by  means  of  which  the  pressure  of  the  atmosphere  may  be  made  to 

lift  quite  a  heavy  weight.     It  consists  of  a  stout  glass  cylinder,  C, 

supported  by  a  frame  and  tripod.     Within  the  lower  part  of  the 

cylinder  is  a  closely  fitting  pis- 
ton from  which  the  weight  is 

hung.     A  brass  plate  is  ground 

to  fit  accurately  upon  the  top 

of  the  cylinder.     This  plate  is 

perforated  and  a  flexible  tube, 

B,  connects  the  cylinder  with 

an   air-pump.     When  the  air 

is  exhausted  from  the   cylin- 
der, the  atmospheric  pressure 

on   the  lower  surface  of   the 

piston   raises  the  piston  and 

supported  weight  the  length 

of  the  cylinder. 

(12.)    The  Magdeburg  hemi- 
spheres   are    made   of    metal. 

They  are  hollow,  and  generally 

three  or  four  inches  in  diam- 
eter.   Their  edges  are  provided 

with  projecting  lips  which  fit 

one  over    the    other.      These 

edges  fit  one  another  air-tight ; 

the   lips  prevent  them    from  FIG.  no. 


LIFTING '-P  UMP. 


175 


FIG.  in. 


moving  sidewise.  The  edges  being  greased  and  placed  together,  the 
air  is  exhausted  from  the  hollow  globe  through  a  tube  provided 
with  a  stop-cock  and  screw.  When  the  air  has  been 
pumped  out,  close  the  stop -cock,  remove  the  hemi- 
spheres from  the  pump,  and  screw  a  convenient 
handle  upon  the  lower  hemisphere,  the  upper  one 
being  provided  with  a  permanent  handle.  It  will 
be  found  that  a  considerable  force  is  necessary  to 
pull  the  hemispheres  asunder.  This  force  is  equal 
to  the  atmospheric  pressure  upon  the  circular  area 
inclosed  by  the  edges  of  the  hemispheres.  If  this 
area  be  ten  square  inches  it  will  require  a  pull  of 
150  pounds  to  separate  the  hemispheres. 

(13.)  Partly  fill  two  bottles  with  water.  Connect 
them  by  a  bent  tube  which  fits 
closely  into  the  mouth  of  one  and 
loosely  into  the  mouth  of  the  other.  Place  the  bot- 
tles under  the  receiver  and  exhaust  the  air.  Water 
will  be  driven  from  the  closely  stoppered  bottle 
into  the  other.  Readmit  air  to  the  receiver  and  the 
water  thus  driven  over  will  be  forced  back. 


294.  The  Lifting  FlG  II2 
Pump.— The  lifting-, 
pump  consists  of  a  cylinder  or  bar- 
rel, piston,  two  valves,  and  a  suc- 
tion pipe,  the  lower  end  of  which 
%Sj  dips  below  the  surface  of  the  liquid 
to  be  raised.  The  arrangement  is 
essentially  the  same  as  in  the  air- 
pump.  As  the  piston  is  worked, 
the  air  below  it  is  gradually  re- 
moved. The  downward  pressure  on 
the  liquid  in  the  pipe  being  thus 
removed,  the  transmitted  pres- 
sure of  the  atmosphere,  exerted; 
upon  the  surface  of  the  liquid, 
pushes  the  liquid  up  through 


FIG. 


176 


FORCE-PUMP. 


the  suction  pipe  and  the  lower  valve  into  the 
barrel.  "When  the  piston  is  again  pressed  down,  the  lower 
valve  closes,  the  reaction  of  the  water  opens  the  piston 
valve,  the  piston  sinking  below  the  surface  of  the  liquid  in 
the  barrel.  When  next  the  piston  is  raised,  it  lifts  the 
water  above  it  toward  the  spout  of  the  pump.  At  the  same 
time,  atmospheric  pressure  forces  more  liquid  through  the 
suction  pipe  into  the  barrel. 

295.  Notes  and  Queries. — The  cistern  or  well  containing 
the  liquid  must  not  be  cut  off  from  atmospheric  pressure,  i.  e.,  must 
not  be  made  air-tight.  Why  ?  For  water  pumps,  the  suction  pipe 
must  not  be  more  than  34  feet  high.  Why  ?  Owing  to  mechanical 
imperfections  chiefly,  the  practical  limit  of  the  water  pump  is  28 
vertical  feet.  As  the  lifting  of  the  liquid  above  the  piston  does  not 
depend  upon  atmospheric  pressure,  water  may  be  raised  from  a  very 
deep  well  by  placing  the  barrel,  with  its  piston  and  valves,  within 
28  feet  of  the  surface  of  the  water,  and  providing  a  vertical  dis- 
charge pipe  to  the  surface  of  the  ground.  The  piston-rod  may 
work  through  this  discharge  pipe.  Deep  mines  are  frequently 
drained  by  using  a  series  of  pumps,  one 
above  the  other,  the  handles  (levers)  of 
which  are  worked  by  a  single  vertical  rod. 
The  lowest  pump  empties  the  water  into  a 
reservoir,  from  which  the  second  pump  lifts 
it  to  a  second  reservoir,  and  so  on. 

296.  The   Force-Pump — In 

the  force-pump,  the  piston  is  generally 
made  solid,  i.  e.,  without  any  valve. 
The  upper  valve  is  placed  in  a  dis- 
charge pipe  which  opens  from  the  bar- 
rel at  or  near  its  bottom.     When  the 
piston  is  raised,  water  is  forced  into 
=  the    barrel  by  atmospheric   pressure. 
I^EE      ~~  When  the  piston  is  forced  down,  the 
FIG.  114.  suction  pipe  valve  is  closed,  the  water 


SIPHON. 


177 


being  forced  through  the  other  valve  into  the  discharge 
pipe.  When  next  the  piston  is  raised,  the  discharge  pipe 
valve  is  closed,  preventing  the  return  of  the  water  above 
it,  while  atmospheric  pressure  forces  more  water  from  below 
into  the  barrel. 

297.  The  Air- Chamber  of  a 
Force-Pump. — Water'  will  be  thrown 
from  such  a  pump  in  spurts,  correspond- 
ing to  the  depressions  of  the  piston.  A 
continuous  flow  is  secured  by  connect- 
ing the  discharge  pipe  with  an  air- 
chamber.  This  air-chamber  is  provided 
with  a  delivery  pipe,  the  lower  end  of 
which  terminates  below  the  surface  of  the 
water  in  the  air-chamber.  When  water  is 
forced  into  the  air-chamber,  it  covers  the 
mouth  of  the  delivery  pipe,  and  compresses 
the  air  confined  in  the  chamber.  This 
diminution  of  volume  of  the  air  is  attended 
by  a  corresponding  increase  of  tension 
(§  284),  which  soon  becomes  sufficient  to 
force  the  water  through  the  delivery  pipe 
in  a  continuous  stream. 


FIG.  115. 


298.  The  Siphon. — The  siphon  consists  of  a  bent 
tube,  open  at  both  ends,  having  one  arm  longer  than  the 
other.  It  is  used  to  transfer  liquids  from  a  higher  to  a 
lower  level,  especially  in  cases  where  they  are  to  be  removed 
without  disturbing  any  sediment  they  may  contain.  It 
may  be  first  filled  with  the  liquid,  and  then  placed  with 
the  shorter  arm  in  the  higher  vessel,  care  being  had  that 
the  liquid  does  not  escape  from  the  tube  until  the  opening 


178  SIPHON. 

C  is  lower  than  mn,  the  surface  of  the  liquid ;  or 
it  may  be  first  placed  in  position, 
and  the  air  removed  by  suction 
at  the  lower  end ;  whereupon,  by 
the  pressure  of  the  atmosphere, 
the  fluid  will  be  forced  up  the 
shorter  arm  and  fill  the  tube.  In 
either  case  a  constant  stream  of 
the  liquid  will  flow  from  the  upper 
PIG>  TI6  vessel  until  the  surface  line  mn  is 

brought  as  low  as  the  opening  in 

the  shorter  arm,  or,  if  the  liquid  be  received  in  another 
vessel,  until  the  level  is  the  same  in  the  two  vessels. 

299.  Explanation  of  the  Siphon. — This  action 
of  the  siphon  may  be  thus  explained:    For  convenience, 
suppose  that  the  sectional  area  of  the  tube  is  one  inch, 
that  the  downward  pressure  of  the  water  in  the  arm  AB 
is  one  pound,  and  that  the  downward  pressure  of  the  water 
in  the  arm  BC  is  three  pounds.     The  upward  pressure  in 
the  tube  at  A  will  equal  the  atmospheric  pressure  on  each 
inch  of  the  surface  mn  outside  the  tube  minus  the  down- 
ward pressure  of  one  pound,  i.  e.,  (15  —  1  =)  14  pounds. 
On  the  other  side,  there  is  at  C  the  upward  atmospheric 
pressure  of  15  pounds,  from  which   must  be  taken  the 
downward  pressure  of  the  water  in  BC,  leaving  a  resultant 
upward  pressure  of  12  pounds  at  C.    The  upward  pressure 
at  A  being  two  pounds  greater  than  that  at  C,  determines 
the  flow  of  the  water  ABC.    The  greater  the  difference 
between  la  and  be,  the  greater  the  velocity  of  the  stream. 

300.  Limitations. — If  the  downward  pressure  at  A 
be  equal  to  the  atmospheric  pressure,  the  liquid  will  not 


SIPHOX. 


179 


flow.  Therefore,  if  the  liquid  "be,  water,  the  height, 
ab,  must  be  less  than  34-  feet ;  if  it  be  mercury,  db 
must  be  less  than  the  mercury  column  of  the  barometer. 

3O1.  Intermittent  Springs.  —  Occasionally  a 
spring  is  found  which  flows  freely  for  a  time,  and  then 
Deases  to  flow  for  a  time.  Fig.  117  represents  an  under- 
ground reservoir,  fed  with  water  through  fissures  in  the 
earth.  The  channel  through  which  the  water  escapes 


FIG.  117. 


FIG.  118. 


from  this  reservoir  forms  a  siphon.  The  water  escaping  at 
the  surface  constitutes  a  spring.  When  the  water  in  the 
reservoir  reaches  the  level  of  the  highest  point  in  the 
channel,  the  siphon  begins  to  act,  and  continues  to  do  so 
until  the  water  level  in  the  reservoir  falls  to  the  mouth  of 
the  siphon.  The  spring  then  ceases  to  flow  until  the 
water  has  regained  the  level  of  the  highest  point  of  the 
siphon-like  channel.  This  action  is  well  illustrated  by 
«  Tantalus'  Cup,"  represented  in  Fig.  118. 

EXERCISES. 

1.  How  high  can  water  be  raised  by  &  perfect  lifting-pump,  when 
the  barometer  stands  at  30  inches  ?    (See  §  253,  [2].) 


180  SIPHON. 

2.  If  a  lifting-pump  can  just  raise  water  28  ft.,  how  high  can  it 
raise  alcohol  having  a  specific  gravity  of  0.8  ? 

3.  Water  is  to  be  taken  over  a  ridge  12.5  m.  higher  than  the  sur- 
face of  the  water,     (a.)  Can  it  be  done  with  a  siphon?    Why  ?    (6.) 
With  a  lifting-pump  ?    Why  V    (c.)  With  a  force-pump  ?    Why  ? 

4.  How  high  will  bromine  stand  in  an  exhausted  tube,  when  mer 
cury  stands  755 mm.t    (Sp.  gr.  of  bromine  =  2.9G.) 

5.  If  water  rises  34  feet  in  an  exhausted  tubo,  how  high  will 
sulphuric  acid  rise  under  the  same  circumstances  ? 

6.  The  sectional  area  of  the  piston  of  a  "  weight-lifter"  being  15 
sq.  inches,  what  weight  could  the  instrument  raise  ? 

7.  If  the  capacity  of  the  barrel  of  an  air-pump  is  \  that  of  the  re- 
ceiver, (a.)  what  part  of  the  air  will  remain  in  the  receiver  at  the 
end  of  the  fourth  stroke  of  the  piston,  and  (b.)  how  will  its  tension 
compare  with  that  of  the  external  air  ? 

8.  How  high  could  a  liquid  with  a  sp.  gr.  of  1.35  be  raised  by  a 
lifting-pump  when  the  barometer  stands  29.5  inches  ? 

9.  Over  how  high  a  ridge  can  water  be  continuously  carried  in  a 
siphon,  the  minimum  standing  of  the  barometer  being  09  cm.  ? 

10.  What  is  the  greatest  pull  that  may  be  resisted  by  Magdeburg 
hemispheres  (a.)  4  inches  in  diameter?  (&.)  8  cm.  in  diameter?    (See 
Appendix  A.) 

.  Recapitulation* — In  this  section  we  have  considered 
the  Air-pump ;  the  Limits  of  Exhaustion  at- 
tainable by  the  ordinary  air-pump ;  Sprengel's  and 
Bunsen's  air-pumps;  the  Condenser  and  Trans- 
ferrer;  numerous  Experiments  pertaining  to  aeri- 
form pressure  and  tension;  the  Lifting-pump;  the 
Force-pump;  the  Siphon  and  Intermittent 
Springs. 

EEVIEW  QUESTIONS  AND  EXERCISES. 

1.  Define  (a.}  Physics,  (& )  Chemistry,  (c.)  Atom,  (d.)  Molecule,  (e.) 
Solids,  (/.)  Liquids  and  (g.)  Aeriform  Bodies. 

2.  Define  (a.)  Inertia,  (&.)  Impenetrability  and  (c.)  Hardness,  illus- 
trating each  by  examples. 

3.  («.)  Define  Momentum  and  (&.)  Energy.     A  body  weighs  500 
Ibs.,  and  has  a  velocity  of  60  ft.  per  second  ;  (c.)  what  is  its  momen 
turn  and  (d.)  what  its  energy  ?     (e.)  How  would  each  be  affected  by 
doubling  the  weight  ?    (/.)  By  doubling  the  velocity  ? 


REVIEW.  181 

4.  Give  (a.)  the  facts  and  (6.)  the  laws  of  gravity.     A  body  weighs 
1440  Ibs.  at  the  surface  of  the  earth  ;  (c.)  how  far  above  the  surface 
will  its  weight  be  90  Ibs.  ?     (d.)  What  will  it  weigh  2200  miles 
below  the  surface  ? 

5.  (a.)  What  is  a  machine?    (&.)  What  is  a  foot  pound?    (c.)  Tell 
how  the  advantage  gained  by  a  simple  mechanical  power  is  found  ; 
and  (d.)  show  this  by  an  illustration  of  your  own.     (e  )  Explain  the 
cause  of  friction. 

6.  (a.)  What  is  a  simple  pendulum  ?    (6.)  What  is  an  oscillation? 
(c.)  How  does  a  change  of  latitude  change  the  number  of  vibrations  ? 
(d.)  Why? 

7.  («.)  What  is  the  length  of  a  second's  pendulum  ?    (6.)  What 
is  the  length  of  one  vibrating  |  seconds  ? 

8.  (a.)  State  the  general  law  of  machines,  and  (6.)  illustrate  it  by 
means  of  the  pulley. 

9.  (a.)  What  is  the  centre  of  gravity  ?    (6.)  How  found? 

10.  (a.)  Draw  figures  illustrating  the  position  of  parts  in  the  dif- 
ferent kinds  of  levers ;   (6.)  make  and  solve  a  simple  problem  in 
each. 

11.  (a.)  What  is  the  relation  which  the  length  of  a  pendulum 
bears  to  its  time  of  oscillation  ?    (6.)  Give  the  length  of  a  pendulum 
beating  once  in  2i  seconds. 

12.  (a.)  Give  the  second  and  third  laws  of  motion,  and  (&.)  illus- 
trate them. 

13.  A  and  B,  at  opposite  ends  of  a  bar  6  ft.  long,  carry  a  weight 
of  600  pounds  suspended  between  them.     A's  strength  being  twice 
as  great  as  B's,  how  far  from  A  must  the  weight  be  suspended  ? 

14.  (a.)  Give  the  formulas  for  falling  bodies,  (&.)  translating  them 
into  common  language.      (c.)    Give  the  same    for  bodies  rolling 
freely  down  inclined  planes.     A  body  fell  from  a  balloon  one  mile 
above  the  surface  of  the  earth  ;  (d.)  in  what  time,  and  (e.)  with  what 
velocity  would  it  reach  the  earth  ? 

15.  A  ball  thrown  downward  with  a  velocity  of  35  feet  per  second 
reaches  the  earth  in  12  i  seconds,     (a.)  How  far  has  it  moved,  and 
(&.)  what  is  its  final  velocity  ? 

16.  (a.)  A  bricklayer's  laborer  with  his  hod  weighs  170  pounds  ; 
he  puts  into  the  hod  20  bricks  weighing  7  pounds  each  ;   he  then 
climbs  a  ladder  to  a  vertical  height  of  30  feet.     How  many  units  of 
work  does  he?    (&.)  If  he  can  do  158,100  units  of  work  in  a  day, 
how  many  bricks  will  he  take  up  the  ladder  in  a  day  ? 

17.  Define  three  accessory  properties  of  matter. 

18.  How  much  weight  will  a  cubic  meter  of  any  solid  lose  when 
weighed  (a.}  in  hydrogen?  (&.)  in  air?  (c.)  in  carbonic  acid  gas? 


182  REVIEW. 

19.  Can  you  devise  a  plan  by  which  an  ordinary  mercurial  barom 
eter  may  be  used  to  measure  the  rarefaction  secured  by  an  air-pump  ? 

20.  (a.)  Give  the  laws  of  liquid  pressure,  and  (&. )  find  the  pressure 
on  one  side  of  a  cistern  filled  with  water,  5  feet  square  and  12  feet 
high  ? 

21.  (a.)  What  is  specific  gravity?    (6.)  What  the  standard  for 
liquids  and  solids?    (c.)  How  is  the  sp.  gr.  of  solids  found? 

22.  Calculate  the  atmospheric  pressure  upon  a  man  having  a  body 
surface  of  16,000  sq.  cm. 

23.  What  is  the  upward  pull  of  a  balloon  of  1,000  cu.  m.,  when 
filled  with  gas  half  as  heavy  as  air,  its  own  weight  being  25  Kg.  ? 

24.  (a.)  State  Archimedes'  principle.     (&.)  How  may  it  be  experi- 
mentally verified  ?    (c.)  In  finding  specific  gravity,  what  is  always 
the  dividend  and  what  is  always  the  divisor  ?    (d.)  A  specific  gravity 
bulb  weighs  88  g.  in  air,  28  g.  in  water,  and  20  g.  in  an  acid.     Find 
the  sp.  gr.  of  the  acid. 

25.  (a.)  Describe  an  overshot  water -wheel,  and  (&,)  give  a  drawing. 

26.  (a.)  Define  the  three  kinds  of  equilibrium,     (b.)  Where  is  the 
centre  of  gravity  in  a  ring?    (c.)  Why  are  lamps,  clocks,  etc.,  pro- 
vided with  heavy  bases  ? 

27.  Find  the  weight  in  sulphuric  acid  (sp.  gr.  1.75)  of  a  piece  of 
lead  weighing  150  g.,  and  having  a  sp.  gr.  of  11. 

28.  A  pendulum  1  meter  long  makes  40  oscillations  in  a  given 
time  ;  how  long  must  a  pendulum  be  to  make  60  oscillations  in  the 
same  time  and  at  th'e  same  place  ? 

29.  (a.)  Give  Mariotte's  law.     (&.)  How  high  could  a  fluid  having 
a  sp.  gr.  of  1.35  be  raised  in  a  common  pump  when  the  barometer 
stands  at  29.5  inches  ? 

30.  Represent,  by  drawings  in  section,  the  essential  parts  of  (a.) 
an  air-pump,  (&.)  a  lifting-pump,  and  (c.)  a  force-pump,    (d.)  Why 
does  the  water  rise  in  the  suction   pipe  of  a  lifting-pump?    (c.) 
What  is  the  immediate  force  that  throws  water  in  a  steady  stream 
from  a  force-pump  ? 

81.  Water  flows  from  an  orifice  25  feet  below  the  surface  of  the 
water,  and  144.72  feet  above  the  level  ground.  Find  the  range  of 
the  jet. 

32.  State  briefly,  by  diagram  or  otherwise,  the  distinguishing 
features  of  solid,  liquid  and  aeriform  bodies. 


MAGNETISM    AND    ELECTRICITY. 


MAGNETS. 

Note. — A  desire  to  secure  favorable  atmospheric  conditions  for 
experiments  in  frictional  electricity  has  determined  the  order  in 
which  the  following  branches  of  physics  are  taken  up.  In  most 
places  in  this  country,  the  school-year  begins  with  September.  In 
such  cases,  this  chapter  would  probably  be  reached  by  January, 
during  which  month  the  atmosphere  is  generally  dry.  Under  other 
circumstances,  the  consideration  of  these  subjects  would  better  be 
omitted  until  sound,  heat,  and  light  have  been  studied. 

302.  Natural  Magnet. — The  mineral  called  load- 
stone is  the  only  known  natural  magnet.    It  is  an  ore  of 
iron,  composed  of  iron  and  oxygen.     //  a  piece  of  load- 
stone  be  rolled  in  iron  filings,  some  of  the  filings 
luill  cling  to  the  loadstone  when  it  is  removed. 

303.  Artificial  Magnets. — Artificial  magnets  are 

usually  made  of  steel.  They  have 
all  the  properties  of  natural  mag- 
nets, are  more  powerful  and  con- 
venient. They  are,  therefore,  pref- 
erable for  general  use.  The  most 

common  forms  are  the  straight  or  bar  magnet  and  the 
horseshoe  magnet.     The  first  of  these  is  a  straight  bar  of 


FIG.  119. 


184 


MAGNETS. 


steel;  the  second  is  shaped  like  a  letter  U,  the  ends  being 
thus  brought  near  together,  as  shown  in  Fig.  119. 

3O4.  Distribution  of  Magnetic  Force.— If  a 

bar  magnet  be  rolled  in  iron  filings  and  then  withdrawn, 
the  filings  cling  to  the  ends  of  the  bar  but  not  to  the 
middle.  This  peculiar  form  of  attraction  is  not  evenly 


FIG.  120. 

distributed  throughout  the  bar.  It  is  greatest  at  or 
near  the  ends.  These  points  of  greatest  attraction  are 
called  the  poles  of  the  magnet. 

3O5.  Attraction  between  a  Magnet  and  Or- 
dinary Iron. — Bring  either  end  of  a  bar  magnet  near 
the  end  of  a  piece  of  iron ;  the  iron  is  attracted.  Bring 
the  same  end  of  the  magnet  near  the  middle  of  the  iron  ; 
the  iron  is  attracted.  Bring  the  same  end  of  the  magnet 


MAGNETS. 


185 


near  the  other  end  of  the  iron ;  the  iron  is  attracted. 
Eepeat  the  experiments  with  the  other  end  of  the  magnet ; 
in  each  case  the  iron  is  attracted.  From  these  experiments 
we  have  a  right  to  conclude  that  either  pole  of  a  magnet 
will  attract  ordinary  iron. 

306.  Attraction  between  Two  Magnets.— 
Freely  suspend  three  bar  magnets,  A,  B  and  (7,  at  some 


FIG.  121. 


distance  from  each  other.  (Place  each  magnet  in  a  stout 
paper  stirrup  supported  by  a  cord ;  or  place  each  upon  a 
board  or  cork  floating  on  water.)  When-  they  have  come  to 
rest,  each  will  lie  in  a  north  and  south  line.  Magnets  are 
chiefly  characterized  by  the  property  of  attracting  iron  and 
this  tendency  to  assume  a  particular  direction  of  position 
when  freely  suspended.  Mark  the  north  end  of  each  sus- 
pended magnet  — ,  and  the  south  end  of  each,  +.  (§  317.) 

(a.)  Take  the  magnet  A  from  its  support,  and  bring  its  +  end  near 
the  —  end  of  B  or  (7.     Notice  the  attraction.    (6.)  Bring  the  +  end 


186  MAGNETS. 

of  A  near  the  +  end  of  B  or  C.  Notice  the  repulsion,  (c.)  Bring 
the  —  end  of  A  near  the  —  end  of  B  or  C.  Notice  the  repulsion. 
(d.)  Bring  the  —  end  of  A  near  the  +  end  of  B  or  C.  Notice  the 
attraction.  (Fig.  121.)  (e.)  From  experiment  (a)  we  learned  that 
the  —  ends  of  B  and  C  were  each  attracted  by  the  +  end  of  A . 
Bring  the  —  end  of  B  near  the  —  end  of  C.  Notice  that  they  now 
repel.  (/.)  From  experiment  (&)  we  learned  that  the  +  ends  of  B 
and  C  were  each  repelled  by  the  +  end  of  A.  Bring  the  +  end  of 
B  near  the  +  end  of  (7.  Notice  that  they  now  repel,  (g.)  In  similar 
manner  show  that  the  +  end  of  B  will  attract  the  —  end  of  C; 
that  the  —  end  of  B  will  attract  the  +  end  of  C.  (See  Appendix  I.) 

From  these  experiments  we  have  a  right  to  conclude  that 
every  magnet  has  two  dissimilar  poles ;  that  like 
poles  repel  each  other ,  but  that  unlike  poles  attract 
each  other. 

Note. — In  all  of  these  experiments  we  deal  with  a  cause  capable 
of  producing  motion.  Hence  (§  64),  magnetism  is  a  force. 

3O7.   Effect   of  Breaking  a  Magnet.—//  a 

magnet  ~be  broken,  each  piece  becomes  a  magnet  with 
two  poles  and  an  equator  of  its  own. .  These  pieces  may  be 
repea'e:11y  subdivided  and  each  fragment  will  be  a  perfect 


FIG.  122. 

magnet.  It  is  probable  that  every  molecule  has  its  poles, 
or  is  polarized,  and  that,  could  one  be  isolated,  it  would 
be  a  perfect  magnet.  "We  thus  conceive  a  magnet  as  made 
up  of  molecules  each  of  which  is  a  magnet,  the  action  of 
the  molar  magnet  being  due  to  the  combined  action  of  all 
the  molecular  magnets  of  which  it  is  composed. 

3O8.  Theory  of  Magnetism.— For  the  explanation  of  the 
phenomena  that  we  have  noticed,  the  existence  of  two  magnetic 
fluids  has  been  imagined.  The  fluid  whose  resultant  effects  are 
manifested  at  the  +  end  of  the  magnet  is  called  the  positive  fluid  ; 


MAGNETS.  187 

in  the  same  way  the  other  is  called  the  negative  fluid.  It  is  imag- 
ined that  each  of  these  two  fluids  repels  its  like  and  attracts  its 
opposite  ;  that  neither  can  exist  without  the  other,  every  magnet 
possessing  equal  quantities  of  both ;  that,  owing  to  their  mutual 
attraction,  they  tend  to  combine  in  or  around  each  molecule  and 
thus  neutralize  each  other  ;  that  they  may  be  separated  by  a  force 
greater  than  their  mutual  attraction,  and  made  to  arrange  them- 
selves in  a  certain  position  in  or  about  the  molecules  to  which  they 
belong,  but  that  they  cannot  be  removed  from  them.  In  this  way 
we  imagine  to  our  minds  the  formation  of  a  magnet  by  bringing 
together  rows  of  polarized  molecules,  whose  similar  poles  are 

turned  in  the  same   direction. 

The  magnetic  separation  thus 
FIG.  123.  imagined  is  represented  in  Fig. 

123.  The  effects  of  the  opposite 

polar  fluids  neutralize  each  other  at  the  middle  of  the  bar,  but  are 
manifested  at  opposite  ends  of  the  bar.  (§  335.) 

309.  A  Hypothetical  Theory.— The  theory  sketched  in 
the  preceding  paragraph  has  value  because  it  connects  the  various 
phenomena  of  magnetism.     But  we  must  remember  that  it  is  only 
a  hypothesis,  and  is  seriously  doubted  by  scientific  men.    Neither 
itTnbr  its  companion,  the  Theory  of  Electric  Fluids,  can  be  re- 
ceived unsuspectingly  until  they  can  connect  the  phenomena  of 
magnetism  and  electricity  one  with  the  other,  and  both  of  them 
with  the  phenomena  of  heat  and  light.     Although  as  yet  they  can- 
not do  this,  we  may  use  them  with  profit  unless  we  allow  ourselves 
to  accept  them  with  a  confidence  that  blinds  our  sight  to  the 
approach  of  something  better. 

310.  Magnetic  and  Diamagnetic  Substances.— Sub- 
stances that  are  attracted  by  a,  magnet  are  called  magnetic;  e.g.,  iron 
or  steel  and  nickel.     Substances  that  are  repelled  by  a  magnet  are 
called  diamagnetic;  e.  g ,  bismuth,  antimony,  zinc,  tin,  mercury, 
lead,  silver,  copper,  gold  and  arsenic.     Of  these,  iron  is  by  far  the 
most  magnetic,  while  bismuth  is  the  most  diamagnetic.     The  mag- 
netic properties  of   iron  or  steel  are  easily  shown  ;  diamagnetic 
properties  require  a  powerful  magnet  for  satisfactory  illustration. 

311.  Magnetic  Induction. — If  a  bar  of  soft  iron 
be  brought  near  one  of  the  poles  of  a  strong  magnet,  it 
becomes,  for  the  time  being,  a  magnet.     The  poles  of  the 


188  MAGNETS. 

temporary  magnet  will  be  opposite  to  those  of  the  perma- 
nent magnet.  The  molecules  of  the  iron  seem  to  be 
polarized  by  the  force  of  the  magnet  when  brought  within 
the  limited  range  of  that  force.  The  combined  fluid  is 
separated  in  each  molecule,  because  the  fluid  acting  at  the 
pole  of  the  magnet  attracts  its  opposite  and  repels  its  like, 
and  this  separating  influence  is  greater  than  the  mutual 
attraction  of  the  two  fluids  thus  torn  asunder.  The  iron 
is  said  to  be  magnetized  by  induction.  If  the  distance 
between  the  iron  and  the  magnet  be  diminished,  the 
inductive  influence  is  thereby  increased.  Actual  contact 
is  not  necessary,  but  when  the  iron  and  the  magnet 
touch,  this  inductive  force  is  the  greatest.  This  force, 
like  other  forms  of  attraction,  varies  inversely  as  the 
square  of  the  distance  (§  100  [2]). 

312.  Illustrations  of  Magnetic  Induction.— (a.)  When 
a  piece  of  soft  iron,  as  a  nail  or  ring,  is  brought  near  the  end  of  a 
magnet,  the  molecules  of 
the  iron  are  polarized  (i.  e., 
their  magnetic  fluids  are 
separated),  and  the  iron  be- 
comes a  magnet  for  this 
reason.  When  the  ring 
touches  the  magnet  it  will 
be  supported.  Bring  a 
second  ring  near  the  first 
ring.  The  action  of  the 
first  ring,  which  is  a  mag- 
net now,  polarizes  the  pI(, 
Second  ring  and  thus  ren- 
ders it  a  magnet  also.  Let  it  touch  the  first  ring  magnet  and  it 
will  be  supported.  In  this  way  quite  a  number  of  rings  (Fig.  124) 
may  be  supported,  each  ring  in  turn  being  thus  magnetized  by  its 
predecessor.  Of  course,  the  attractive  and  repulsive  forces  are  con- 
tinually weakening  from  the  first  to  the  last  ring.  Now  support 


MAGNETS.  189 

the  upper  ring  upon  your  finger,  and  remove  the  magnet.  The 
force  that  separated  the  fluids  in  the  molecules  of  the  first  ring  and 
held  them  apart  is  no  longer  present ;  those  fluids,  therefore,  rush 
together.  There  is  now  no  cause  capable  of  holding  apart  the 
opposite  fluids  in  the  molecules  of  the  second  ring,  and  they  con- 
sequently rush  together  ;  and  so  in  the  case  of  each  ring. 

(&.)  Suspend  an  iron  key  from  the  positive  end  of  a  bar  magnet. 
The  key  is  inductively  magnetized,  the  relation  of  its  poles  to  each 
other  and  to  the  magnet  being  as  shown  in  Fig.  125.  A  second 


FIG.  125. 


bar  magnet  of  about  the  same  power,  with  its  poles  opposite,  is 
moved  along  the  first  magnet.  When  the  —  end  of  the  second 
magnet  comes  over  the  key,  the  key  drops.  The  +  pole  of  the 
lower  magnet  attracted  the  —  and  repelled  the  +  of  the  key.  The 
—  pole  of  the  upper  magnet  had  an  opposite  effect,  and  as  the  two 
magnets  were  of  the  same  power,  or  nearly  so,  the  separating  influ- 
ence became  less  than  the  mutual  attraction  of  the  opposite  fluids, 
which  consequently  reunited.  This  experiment  goes  to  show  that 
when  a  magnetic  body  is  attracted  by  a  magnet,  the  attraction  is 
preceded  ly  polarization. 

313.  Magnetic  Curves. — The  inductive  influence 
of  a  magnet  upon  iron  is  not  affected  by  the  interposition 
of  any  non-magnetic  body.  Over  a  good  bar  magnet  place 
a  piece  of  card -board,  upon  which  sprinkle  iron  filings; 
tap  the  card-board  lightly.  The  "magnetic  curves" 
(Fig.  126)  thus  formed  are  very  interesting  and  instruc- 
tive. The  filings  in  any  one  of  these  curves  are  temporary 
magnets  with  adjoining  poles  opposite  and  therefore  attrac- 
ting. By  using  two  bar  magnets  placed  side  by  side,  first, 
with  like  poles  near  each  other,  and,  secondly,  with  unlike 


190 


MAGNETS. 


FIG.  126. 

poles  near  each  other,  their  combined  effect  on  the  iron 
filings  may  be  easily  observed. 

314.  Magnetic  Needles.— A 

bar  magnet  may  be  supported  by 
balancing  it  upon  a  pivot,  by  sus- 
pending it  by  a  fine  untwisted  thread, 
by  floating  it  upon  water  by  means 
of  a  cork,  and  in  several  other  ways. 
*4.  small  bar  magnet  suspended  FIG.  127. 

in  such  a  manner  as  to 
allow  it  to  assume  its  cho- 
sen position  is  a  magnetic 
needle.  (See  Appendix  J.) 


(«.)  If  it  be  free  to  move  in  c. 
horizontal  plane  it  is  a  horizontal 
needle  ;  e.  g. ,  the  mariner's  or  the 
surveyor's  compass  (Fig.  127).  It 
will  come  to  rest  pointing  nearlv 
north  and  south.  If  the  magnet  be 
free  to  move  in  a  vertical  plane  it 
constitutes  a  vertical  or  dipping 
needle  (Fig.  128).  Two  magnets 
fastened  to  a  common  axis  but  hav- 
ing their  poles  reversed  constitute 


FIG.  128. 


MAGNETS. 


191 


an  astatic  needle  (Fig.  129).  An  astatic 
needle  assumes  no  particular  direction 
with  respect  to  the  earth.  (§  391.) 

315.  Terrestrial  Magnet- 
ism.— If  a  small  dipping  needle  be 
placed  over  the  —  end  of  a  bar  mag- 
net, the  needle  will  take  a  vertical 
position  with  its  -f  end  down  (Fig. 
130).  As  the  needle  is  moved  toward  the  other  end  of  the 
bar  it  turns  from  its  vertical  position.  When  over  the 


FIG.  129. 


FIG.  130. 

neutral  line,  the  needle  is  horizontal.  As  it  approaches  the 
+  end  of  the  magnet  the  needle  again  becomes  vertical, 
but  the  —  end  of  the  needle  is  drawn  down.  If  a  dipping 
needle  be  carried  from  far  southern  to  far  northern  lati- 
tudes it  will  act  in  a  similar  way.  These  facts  seem  to 
teach  that  the  earth  is  a  great  magnet  with  magnetic 
poles  near  its  geographical  poles.  The  magnetic  pole 
in  the  northern  hemisphere  was  found  in  1832  by  Capt. 
Ross.  It  is  a  little  north  and  west  of  Hudson's  Bay,  in 
latitude  70°  05'  N.,  and  longitude  96°  45'  W.  A  place  in 
the  southern  hemisphere  has  been  found  where  the  needle 
is  nearly  vertical. 

316.  The  Earth's  Inductive  Influence.— That 

the  earth  is  really  a  magnet  is  further  shown  by  its  indue- 


192 


MAGNETS. 


tive  influence.  An  iron  bar  placed  in  the  position 
assumed  by  the  dipping  needle  and  struck  a  sharp 
blow  on  the  end  becomes  polarized.  The  magnetic  in- 
fluence of  the  bar  may  be  tested  by  moving  a  small  mag- 
netic needle  along  its  length,  and  noticing  that  one  end  of 
the  bar  attracts  one  end  of  the  needle  and  the  other  the 
other  end.  A  steel  poker  which  has  usually  stood  in  a 
nearly  vertical  position  may  thus  be  shown  to  have  ac- 
quired magnetism. 

317.  Names  of  Magnetic  Poles.— We  have  now  learned 
to  regard  the  earth  as  a  huge  magnet,  with  one  pole  in  the  northern 
hemisphere  and  one  in  the  southern  Since  unlike  poles  attract 
each  other,  it  follows  that  the  earth's  magnetic  pole  situated  in  the 
northern  hemisphere  is  opposite  to  the  end  of  a  magnetic  needle  that 
points  to  the  north.  From  this  fact,  great  confusion  of  nomencla- 
ture has  arisen.  We  have  spoken  of  the  end  of  the  needle  that 
points  north  as  —  or  negative.  Following  this  nomenclature,  the 
northern  magnetic  pole  of  the  earth  must  be  +  or  positive.  (See 
Report  of  the  British  As- 
sociation Committee  on 
Electrical  Standards,  Ap- 
pendix C,  1863.)  But 
popular  usage  calls  the 
north-seeking  end  of  the 
needle  the  north  pole, 
and  the  other  end  the 
south  pole.  This  intro- 
duces great  confusion 
when  we  wish  to  speak 
of  the  magnetic  poles  of 
the  earth.  The  nomen- 
clature that  we  have 
adopted  obviates  this 
confusion. 


318.     Inclina- 
tion   or    Dip. — 

The  angle   that  a 


FIG.  131. 


MAGNETS.  193 

dipping  needle  makes  with  a  horizontal  line  is  called 
its  inclination  or  dip.  At  the  magnetic  poles  the 
inclination  is  90°;  at  the  magnetic  equator  there  is  no 
inclination.  The  inclination  at  any  given  place  is  not 
greatly  different  from  the  latitude  of  that  place. 

319.  Declination  or  Variation. — The  magnetic 
needle,  at  most  places,  does  not  lie  in  a  north  and  south 
line.     The  angle  which  the  needle  makes  with  the 
geographical  meridian  is  its  declination  or  varia- 
tion.   A  line  drawn  through  all  places  where  the  needle 
points  to  the  true  north  is  called  a  Line  of  no  Variation. 
Such  a  line,  nearly  straight,  passes  near  Cape  Hatteras, 
a  little  east  of  Cleveland,  through  Lake  Erie  and  Lake 
Huron.    It  is  now  slowly  moving  westward.    At  all  places 
east  of  the  Line  of  no  Variation,  the  —  end  of  the  needle 
points  west  of  the  true  north ;  at  all  places  west  of  the 
Line  of  no  Variation,  the  variation  is  easterly.    The  fur- 
ther a  place  is  from  this  line,  the  greater  the  declination — 
it  being  18°  in  Maine  and  more  than  20°  in  Oregon. 

320.  Magnetization. — A  common  way  of  magnetizing  a 
steel  bar  is  to  draw  one  end  of  a  strong  magnet  from  one  end  of  the 
bar  to  the  other,  repeating  the  operation  several  times,  always  in  the 
same  direction.    A  second  method  is  to  bring  together  the  opposite 
poles  of  two  magnets  at  the  middle  of  the  bar  to  be  magnetized,  and 
simultaneously  drawing  them  in  opposite  directions  from  the  mid- 
dle to  the  ends.     A  third  method,  represented  in  Fig.  132,  is  known 
as  "the  double  touch."     The  opposite  poles  of  two  magnets  are 
kept  at  a  fixed  distance  from  each  other  by  means  of  a  wooden  block 
placed  between  them.      The  magnets  thus  held  are  moved  from 
the  middle  toward  one  end  of  the  bar,  thence  to  the  other  end, 
repeating  the  operation  several  times,  and  finishing  at  the  middle 
when  each  half  of  the  bar  has  received  the  same  number  of  fric- 
tions.   But  better  than  any  of  these  can  give  are  the  effects  produced 
by  electro-magnetism.    (§  394) 

9 


194 


MAGNETS. 


FIG.  132. 

321.  Armatures. — Magnets  left  to  themselves  would  soon 
lose  their  magnetism  by  the  recombination  of  their  magnetic  fluids, 
They  must  therefore  be  provided  with  armatures. 
Armatures  are  pieces  of  soft  iron  placed  in  contact  with 
opposite  poles,  as  shown  in  Fig.  133.  The  two  poles 
of  the  magnet  (or  magnets,  for  two  bar 
magnets  may  be  thus  protected)  act 
inductively  upon  the  armature  and 
produce  in  it  poles  opposite  in  kind 
to  those  with  which  they  come  in  con- 
tact. The  poles  of  the  armature  in  turn 
react  upon  the  magnet,  and,  by  their 
power  of  attraction,  aid  in  preventing 
the  recombination  of  the  fluids  in  the 
magnet.  The  armature  is  sometimes 
the  iron  axle  of  a  brass  wheel ;  it  is 
then  called  a  rolling  armature.  Hold 
a  horse-shoe  magnet  by  its  middle, 
slightly  depress  the  poles,  place  the 
wheel  upon  the  arms  of  the  magnet  as 
shown  in  Fig.  134,  and  allow  it  to  roll 
to  the  end.  Its  momentum  will  carry  p1G  I3^ 
the  axle  around  the  ends  of  the  mag- 
net, and  the  wheel  will  roll  back  to  the  middle,  with  the  axle  on 
the  under  side  of  the  magnet. 


FIG.  133. 


MAGNETS.  195 


EXERCISES  AND  QUESTIONS. 

1.  (a.)  What  is  a  magnetic  pole?     (b.)  A  magnetic  equator! 
(c.)  How  does  a  magnet  behave  toward  soft  iron?    (d.)  How  does 
soft  iron  behave  toward  a  magnet  ? 

2.  (a.)  State  carefully  the  various  effects  which  one  magnet  may 
exert  upon  a  second  magnet.     (&.)  Generalize  these  observed  facts 
into  a  law. 

3.  (a.)  Give  a  theory  of  magnetism.      (&.)  State  its  merits  and  (c.) 
its  demerits. 

4.  (a.)  Given  a  bar  magnet,  how  would  you  determine  the  sign  of 
either  of  its  poles?    (&.)  What  is  a  diamagnetic  substance  ? 

5.  (a.)  Illustrate  magnetic  induction,      (b.)  Explain  it.     (c.)  If  a 
magnetic  needle  be  freely  suspended  from  its  centre  of  gravity, 
what  position  will  it  assume? 

6.  (a.)  Do  you  think  that  the  earth  is  a  magnet  ?    (&.)  Give  a  good 
reason  for  your  answer,     (c.)  Do  the  magnetic  and  geographical 
meridians  ever  coincide  ?     (d.)  Do  they  always  coincide  ?    (e.)  If 
they  do  not  coincide,  what  name  would  you  give  to  their  difference 
in  direction  ? 

7.  (a.)  Does  the  magnetic  attraction  of  the  earth  upon  a  ship's 
compass  tend  to  float  the  ship  northward  ?    (b.)  If  so,  why  ?    If  not, 
why  not  ?    (c.)  What  is  an  armature,  and  (d.)  what  is  it  good  for  ? 

8.  (a.)  State  and  illustrate  the  second  law  of  motion,     (b.)  State 
and  illustrate  the  law  of  universal  gravitation,     (c.)  A  body  falls  to 
the  ground  from  rest  in  11  seconds  ;  what  is  the  space  passed  over  ? 

Recapitulation. — In  this  section  we  have  considered 
Natural  and  Artificial  Magnets;  Magnetic 
Poles  ;  the  Attraction  of  a  Magnet  for  Ordi- 
nary Iron  ;  the  Law  of  Magnets  ;  a  Broken 
Magnet ;  the  theory  of  Magnetic  Fluids  and  its 
.value  ;  Magnetic  and  Diamagnetic  substances ; 
magnetic  Induction  with  illustrations;  magnetic 
Curves ;  magnetic  Needles  ;  the  Earth  as  a 
Magnet,  and  its  inductive  influence;  the  Nomen- 
clature of  magnetic  poles ;  Dip  and  Variation  ; 
how  to  Make  Magnets  and  how  to  Keep  them. 


196  FRICTION AL    ELECTRICITY. 


il. 


FRICTIONAL    ELECTRICITY. 

322.  Preparatory.  —  Provide  two  stout  sticks  of  sealing-wax 
and  one  or  two  pieces  of  flannel  folded  into  pads  about  20  em. 
(8  inches)  square  ;  two  stout  glass  tubes  closed  at  one  end,  30  or 
40  cm.  in  length  and  about  2  cm.  in  diameter  (long  "  ignition  tubes  ") 
and  one  or  two  silk  pads  about  20  cm.  square,  the  pads  being  three 
or  four  layers  thick  ;  a  few  pith  balls  about  1  cm.  diameter  (whittle 
them  nearly  round  and  finish  by  rolling  them  between  the  palms 
of  the  hands)  ;  a  balanced  straw  about  a  foot    Q  ^ 
long,  represented  in  Fig.  185.     The  ends  of  the                   '« 

straw  carry  two  small  discs  of  paper  (bright  ~IG"  T^' 

colors  preferable)  fastened  on  by  sealing-wax.  The  cap  at  the  mid- 
dle of  the  straw  is  a  short  piece  of  straw  fastened  by  sealing-wax. 
This  is  supported  upon  the  point  of  a  sewing-needle,  the  other  end 
of  which  is  stuck  upright  into  the  cork  of  a  small  glass  vial.  From 
the  ceiling  or  other  convenient  support,  suspend  one  of  the  pith 
balls  by  a  fine  silk  thread.  The  efficiency  of  the  silk  pad  above 
mentioned  may  be  increased  by  smearing  one  side  with  lard  and 
applying  an  amalgam  made  of  one  weight  of  tin,  two  of  zinc,  and 
six  of  mercury.  The  amalgam  which  may  be  scraped  from  bits  of 
a  broken  looking-glass  answers  the  purpose  admirably. 

323.  Electric  Attractions.  —  See  that  the  sealing- 
wax  and  glass  rods,  the  flannel  and  silk  pads  are  perfectly 
dry.     Have  them  quite  warm,  that  they  may  not  condense 
moisture  from  the  atmosphere.     For  a  moment  hriskly  rub 
the  sealing-wax  with  the  flannel  and  bring  the  stick  near 
the  suspended  pith  ball.     The  ball  will  be  drawn  to  the 
wax.     Bring  the  wax  near  one  end  of  the  balanced  straw  ; 
it  may  be  made  to  follow  the  wax  round  and  round. 
Bring  it  near  small  scraps  of  paper,  shreds  of  cotton  and 
silk,  feathers  and  gold  leaf,  bran  and  sawdust,  and  other 
light  bodies;  notice  that  they  are  attracted  to  the  wax. 


FRICTIONAL  ELECTRICITY. 


19? 


FIG.  136. 


Eepeat  all  of  these 
experiments  with  a 
glass  rod  which  has 
been  rubbed  with 
the  silk  pad  (Fig. 
136).  You  may  make 
a  light  paper  hoop 
or  an  empty  egg-shell 
roll  after  your  rod. 
Place  an  egg  in  a 
wineglass  or  egg  cup.  Upon  its  end  balance  a  meter  stick 
or  a  common  lath.  The  end  of  the  stick  may  be  made 
to  follow  the  rubbed  rod  round  and  round.  Place  the 
blackboard  pointer  or  other  stick  in  a  stiff  paper  stirrup 
suspended  by  a  stout  silk  thread  or  narrow  silk  ribbon. 
It  may  be  made  to  imitate  the  actions  of  the  balanced 
straw  or  lath.  Now  read  §  64. 

324:.  Electric  Repulsion. — The  suspended  pith, 
ball  is  called  an  electric  pendulum.  Bring  the  rubbed 
glass  rod  near  the  pith  ball  again.  It  will  attract  the  ball 
as  we  have  already  seen  in  the  last  paragraph  (Fig.  137). 
Allow  the  ball  to  touch  the  rod  and  notice  that  in  a  mo- 
ment the  ball  is  thrown  off.  If  the  ball  be  pursued  with 
the  rod,  it  will  be  found  that  the  rod  that  a  moment  ago 
attracted  now  repels  it  (Fig.  138).  Touch  the  ball  with 
the  finger ;  it  successively  seeks  the  rod,  touches  the  rod, 
flies  from  the  rod.  Repeat  the  experiments  with  the 
sealing-wax  after  it  has  been  rubbed  with  flannel.  Rub 
the  glass  rod  with  silk  and  bring  it  over  the  small  scraps 
of  paper ;  notice  that  after  the  attraction  the  paper  bits 
do  not  merely  fall  down,  they  are  thrown  down. 


198 


FRICTIONAL  ELECTRICITY. 


FIG.  137. 


FIG.  138. 


325.  Electric   Force.— We   must   by  this    time 
recognize  the  fact  that  we  are  dealing  with  a  new  class  of 
phenomena.     We  have  an  agent  here  capable  of  producing 
motion  ;    we  have  indisputable  evidence  of  the  presence 
of  a  force.     This  force  is  called  electricity.    Electricity 
is  a  force  manifested  ~by  the  peculiar  phenomena  of 
attraction  and  repulsion.    It  is  believed  that  electricity 
is  a  form  of  molecular  motion,  but  this  belief  rests  upon 
analogy  rather  than  demonstration. 

326.  Two  Kinds  of  Electricity.— Prepare  two 

electric  pendulums.  Bring  the  electrified  glass  rod  near 
the  pith  ball  of  one ;  after  contact,  the  ball  will  be  repelled 
by  the  glass.  Bring  the  electrified  sealing-wax  near  the 
second  pith  ball ;  after  contact  it  will  be  repelled  by  the 
wax.  Satisfy  yourself  that  the  electrified  glass  will  repel 
the  first;  that  the  electrified  sealing-wax  will  repel  the 
second.  Let  the  glass  rod  and  the  sealing-wax  change 


miCTIONAL  ELECTRICITY.  199 

hands.  The  first  ball  was  repelled  by  the  glass ;  it  will  be 
attracted  ly  the  sealing-ivax.  The  second  ball  was  repelled 
by  the  sealing-wax;  it  will  be  attracted  ly  the  glass. 
These  experiments  clearly  show  that  the  electricity 
developed  on  glass  is  different  in  kind  from  that 
developed  on  sealing-wax.  They  exhibit  opposite 
forces  to  a  third  electrified  body,  each  attracting  what  the 
other  repels. 

327.  The  Two  Electricities  Named.— As  the 

two  kinds  of  electricity  are  opposite  in  character,  they 
have  received  names  that  indicate  opposition.  The  elec- 
tricity developed  on  glass  by  rubbing  it  with  silk  is 
called  positive  or  +  ;  that  developed  on  sealing-wax 
by  rubbing  it  with  flannel  is  called  negative  or  — . 
The  terms  vitreous  and  resinous  respectively  were  formerly 
used. 

328.  Only  Two   Kinds  of  Electricity.— By 

repeating  the  experiments  of  §  326  with  other  substances, 
it  is  found  that  all  electrified  bodies  act  like  either  the 
glass  or  the  sealing-wax. 

329.  The  Law  of  Electric  Action.— By  the 

experiments  already  performed,  we  have  made  evident  the 
fact  that  two  bodies  charged  with  like  electricities 
repel  each  other ;  two  bodies  charged  with  opposite 
electricities  attract  each  other. 

330.  The  Test  for  Either  Kind  of  Electricity.— 

When  the  pith  ball  was  attracted  by  the  rubbed  glass  it  became, 
during  the  time  of  contact,  charged  with  the  +  electricity  of  the 
glass  ;  hence  it  was  repelled.  When  it  was  attracted  by  the  rubbed 
sealing-wax  it  became,  during  the  time  of  contact,  charged  with  the 
—  electricity  of  the  wax  ;  then  it  was  repelled.  But  either  the  wax 
or  the  glass  attracted  the  uncharged  pith  ball.  We  must  therefore 


200 


FRICTIONAL  ELECTRICITY. 


remember  that  attraction  affords  no  safe  test  for  the  kind  of  elec- 
tricity, while  repulsion  does.  If  glass  rubbed  with  silk  repels  a  body, 
that  body  is  charged  with  +  electricity.  If  sealing-wax  rubbed 
with  flannel  repels  a  body,  that  body  is  charged  with  —  electricity. 

331.  Electroscopes. — An  instrument  used  to 
detect  the  pres- 
ence of  electric- 
ity, or  to  deter- 
mine Us  ~kind,  is 
called  an  electro- 
scope. The  elec- 
tric pendulum 
(§  324)  is  a  com- 
mon form  of  the 
electroscope.  Two 
vertical  strips  of 
tissue  paper,  hang- 
ing side  by  side, 
constitute  a  simple 
electroscope.  It  is  well  to  prepare  the  paper  beforehand 
by  soaking  in  a  strong  solution  of  salt  in  water  and  drying. 
The  gold  leaf  electroscope  is  represented  in  Fig.  139.  A 
metallic  rod,  which  passes  through  the  cork  of  a  glass  ves- 
sel, terminates  below  in  two  narrow  strips  of  gold  leaf  and 
above  in  a  metallic  knob  or  plate.  The  object  of  the 
vessel  is  to  protect  the  leaves  from  mechanical  disturb- 
ance by  air  currents.  The  upper  part  of  the  glass  is  often 
coated  with  a  solution  of  sealing-wax  or  shellac  in  alcohol, 
to  lessen  the  deposition  of  aqueous  vapor  from  the  atmos- 
phere. This  instrument  when  well  made  is  very  delicate.  • 


FIG.  139. 


332.  Use  Of  the  Electroscope.— (a.)  The  electric  pendu 
lura  is  used  as  an  electroscope  as  follows  :   If  the  uncharged  pit!* 


FRICTION AL  ELECTRICITY.  201 

ball  is  attracted  by  a  body  brought  near  it,  the  body  is  electrified. 
To  determine  the  sign  of  the  electricity  of  the  body  thus  shown  to 
be  electrified,  the  pith  ball  is  allowed  to  touch  it  and  be  repelled. 
If  now  the  ball  be  repelled  by  a  glass  rod  rubbed  with  silk  (or  by 
any  other  body  known  to  be  positively  charged),  the  pith  ball  and 
the  body  in  question  manifest  +  electricity.  If  the  pith  ball,  after 
repulsion  by  the  body  whose  electricity  is  under  examination,  be 
repelled  by  sealing-wax  rubbed  with  flannel  (or  by  any  other  body 
known  to  be  negatively  charged),  the  pith  ball  and  the  body  in 
question  manifest  —  electricity. 

(&.)  One  way  of  testing  with  the  gold  leaf  electroscope  is  to 
touch  the  knob  or  plate  with  the  electrified  body.  The  knob,  rod 
and  leaves  are  thus  charged  with  the  same  kind  of  electricity, 
and  the  leaves  diverge.  If  the  leaves  be  rendered  more  diver- 
gent by  holding  a  positively  electrified  body  near  the  knob,  the 
original  charge  was  +  ;  if  this  effect  be  produced  by  a  negatively 
charged  body,  the  original  charge  was  — .  This  method  is  objec- 
tionable for  the  reason  that  if  the  original  charge  be  at  all  intense 
it  is  likely  to  tear  the  gold  leaves.  A  safer  method  is  as  follows 
Cautiously  bring  the  electrified  body  near  the  knob ;  the  leaves 
will  diverge.  Touch  the  knob  with  the  finger  ;  the  leaves  will  fall 
together.  Remove  first  the  finger  and  then  the  electrified  body ; 
the  leaves  will  diverge  again.  If  now  the  divergence  of  the  leaves 
be  increased  by  bringing  a  positively  charged  body  near  the  knob, 
the  original  charge  was  — ;  if  the  divergence  be  thus  diminished, 
the  original  charge  was  + .  (See  Appendix,  K.) 

333.  Conductors. — From  a  horizontal  glass  rod  or 
tightly-stretched  silk  cord,  suspend  a  fine  copper  wire,,  a 
linen  thread- and  two  silk  threads,  each  at  least  a  meter 
long.  To  the  lower  end  of  each  attach  a  metal  weight  of 
any  kind.  Place  the  weight  supported  hy  the  wire  upon 
the  plate  of  the  gold  leaf  electroscope.  Bring  the  electri- 
fied glass  rod  near  the  upper  end  of  the  wire ;  the  gold 
leaves  instantly  diverge.  Repeat  the  experiment  with  the 
linen  thread ;  in  a  little  ivliile  the  leaves  diverge.  Repeat 
the  experiment  with  the  dry  silk  thread ;  the  leaves  rlo  not 
diverge  at  all.  Rub  the  rod  upon  the  upper  end  of  the 
silk  thread  ;  no  divergence  at  all.  Wet  the  second  silk 


202  FRICTION AL  ELECTRICITY. 

cord  thoroughly,  and  with  it  repeat  the  experiment ;  the 
leaves  diverge  instantly.  Balance  a  meter  stick  or  common 
lath  upon  a  wine-glass.  About  an  inch  below  one  end  of 
the  stick  support  a  few  bits  of  paper  or  gold  leaf.  To  the 
other  end  of  the  lath  bring  an  electrified  glass  rod.  The 
bits  of  paper  will  be  alternately  attracted  and  repelled  by 
the  stick.  Continue  these  experiments  with  other  sub- 
stances until  you  are  convinced  that  some  substances 
transmit  electricity  readily  and  that  others  do  not. 
Those  that  offer  little  resistance  to  the  passage  of  elec- 
tricity are  called  conductors ;  those  that  offer  great  resist- 
ance are  called  non-conductors  or  insulators.  A  conductor 
supported  by  a  non-conductor  is  said  to  be  insulated. 

334.  Electrics. — Any  substance,  when  insulated, 
may  be  sensibly  electrified ;  but  when  an  uninsulated 
conductor  is  rubbed,  the  electricity  escapes  as  fast  as 
it  is  developed.    Thus  we  see  that  the  old  division  of 
bodies  into  electrics  and  non-electrics,  or  bodies  that  may 
be  electrified  and  those  that  cannot  be  electrified,  is  nothing 
more  than  a  division  into  conductors  and  non-conductors. 

(a )  Suspend  a  copper  globe  or  other  metal  body  by  a  silk  thread 
and  strike  it  two  or  three  times  with  a  cat's  skin  or  fox's  brush. 
Bring  the  gold-leaf  electroscope  near  the  globe.  The  leaves  will 
diverge. 

335.  Theory   of    Electricity.— According  to  one  provi- 
sional theory,  electric  action  is  due  to  two  fluids,  each  self  repulsive ; 

.  both  mutually  attractive  (§§  308,  309).  When  these  opposite  fluids 
(+  and  — )  are  mixed  in  equal  quantities,  they  neutralize  each  other 
and  afford  no  manifestations.  All  bodies  in  the  natural  or  unelec- 
trified  condition  are  pervaded  by  large  quantities  of  this  neutral 
fluid.  By  friction,  chemical  action  and  other  means,  this  fluid  may 
be  decomposed,  its  two  constituents  being  torn  asunder.  One  fluid 
clings  by  preference  to  the  rubber ;  the  other  to  the  body  rubbed. 


FRICTIONAL  ELECTRICITY.  203 

When  a  body  is  electrified,  it  gives  up  a  part  of  one  of  the  fluids 
and  gains  an  equal  amount  of  the  other.  The  change  is  wholly  in 
the  kind  ;  not  at  all  in  the  quantity.  The  body  which  has  an  excess 
of  +  electricity  is  positively  electrified.  This  involves  an  excess  of 
—  electricity  in  some  other  body  which  is  negatively  electrified  at 
the  same  instant.  Hence  the  electricity  of  the  rubber  must  be  of 
the  kind  opposite  to  that  of  the  body  rubbed.  Experiment  confirms 
the  deduction. 

336.  Electric  and  Magnetic  Fluids  Compared.— 

These  two  sets  of  imaginary  fluids  have  many  obvious  points  of 
resemblance,  but  they  have  one  marked  difference.  Neither  mag- 
netic fluid  can  leave  the  molecule  to  which  it  originally  pertained ; 
either  one  of  the  electric  fluids  may  leave  its  molecule  and  be 
replaced  by  a  like  amount  of  its  opposite. 

337.  Induction. — From   several  of  the  preceding 
experiments  we  see  that  actual  contact  with  an  electrified 
body  is  not  necessary  for  the  manifestation   of  electric 
action  in  an  unelectrified  body.    When  an  electrified  body 
C,  is  brought  near  an  insulated  unelectrified  conductor  B, 
the  neutral  fluid  of  the  latter  is  decomposed  by  the  influ- 
ence of  the  former.    The  electricity  of  (7,  repels  one  con- 
stituent of  the  neutral  fluid  in  B  and  attracts  the  other, 
thus  separating  them.    The  second  body,  B,  is  then  said  to 

be  polarized.  The  same  fluids  of 
B,  each  of  which  a  moment  ago 
rendered  the  other  powerless,  are 
still  there  in  full  quantity,  but 
they  have  been  separated  and  each 
clothed  with  its  proper  power. 
This  effect  is  due  to  the  mere 

presence  of  the  electrified  body  (7,  which  is  said  to  decom- 
pose the  neutral  fluid  of  B  by  induction.  When  C  is 
removed,  the  separated  fluids  of  B  again  mingle  and  neu- 
tralize each  other. 


204  FRICTIONAL  ELECTRICITY. 

338.  Analogous  to  Magnetic  Induction.— We 

must  master  this  subject  even  at  the  expense  of  repetition, 


FIG.  141. 

for  induction  is  the  only  stepping-stone  to  an  intelligent 
comprehension  of  what  follows.  If  an  insulated  conductor, 
bearing  a  number  of  pith  ball  (or  paper)  electroscopes,  be 
brought  near  an  electrified  body,  C,  but  not  near  enough 
for  a  spark  to  pass  between  them,  the  pith  balls  near  the 
ends  of  the  conductor  will  diverge,  showing  the  presence 
of  uncombined  electricity.  The  pith  balls  at  the  middle 
of  the  conductor  will  not  diverge,  marking  thus  a  neutral 
line. 

339.  Charging  a  Body  by  Induction.— If  the 

polarized  conductor  be  touched  with  the  hand,  or  other- 
wise placed  in  electric  communication  with  the  earth, 
the  electricity  repelled  by  C  will  escape,  and  the  pith  balls 
at  B  will  fall  together.  The  electricity  at  the  other  end 
will  be  held  by  the  mutual  attraction  between  it  and  its 
opposite  kind  at  C.  The  line  of  communication  with  the 
ground  being  broken,  and  the  conductor  then  removed 
from  the  vicinity  of  C,  it  will  be  found  charged  with  elec- 


FRICT10NAL  ELECTRICITY.  205 

tricity  opposite  in  kind  to  that  of  C.    Thus  a  body  may  be 
charged  by  induction  with  no  loss  to  the  inducing  body. 

340.  Successive  Induction.— If  a  series  of  insu- 
lated conductors  be  placed  in  line  as  shown  in  Fig.  142, 
and  a  positively  electrified  body  be  brought  near,  each 
conductor  will  be  polarized.  The  first  will  be  polarized  by 
the  influence  of  the  -f  of  C\  the  second  by  the  influence 
of  the  +  of  M,  and  so  on. 

(a.}  Either  electricity  from  M  or  N  may  be  carried  by  a  small 
insulated  body,  called  a  proof -plane  (Fig.  158),  to  the  electroscope, 
there  tested  and  found  to  be  as  represented  in  the  figure.  If  the 
conductors  M  and  .ZVbe  now  placed  in  actual  contact,  the  +  of  both 
will  be  repelled  by  G  to  the  furtherest  extremity  of  W  and  the 
—  of  both  attracted  to  the  opposite  end  of  M,  near  to  G. 
C 


FIG.  142. 

(b.)  It  is  very  plain  that  any  body  may  be  looked  upon  as  a  collec- 
tion of  many  parallel  series  of  such  conductors,  each  molecule 
representing  a  conductor.  Thus  each  molecule  may  be  polarized, 
+  on  one  side  and  —  on  the  other.  If  the  body  in  question  be  a 
good  conductor  of  electricity,  this  polarization  of  the  molecules  is  only 
for  an  instant.  The  two  electricities  pass  from  molecule  to  mole- 
cule and  accumulate  at  opposite  ends  of  the  body.  The  body  is 
then  polarized,  but  not  the  molecules  of  the  body.  On  the  other 
hand,  good  insulators  resist  this  tendency  to  transmit  the  electrici- 
ties from  molecule  to  molecule  and  are  able  to  maintain  a  high 
degree  of  molecular  polarization  for  a  great  length  of  time.  In 


206  FRICTION AL  ELECTRICITY. 

brief,  the  molecules  of  conductors  discharge  their  electricities  easily 
into  each  other  ;  those  of  non-conductors  do  not. 

341.  Polarization   Precedes   Attraction.— 

When  an  electrified  glass  rod  is  brought  near  an  insulated 
uncharged  pith  ball  (electric  pendu- 
lum), the  pith  ball  is  polarized  as 
shown  in  the  figure.     As  the  —  of 
the  ball  is  nearer  the  +  of  the  glass 

than  is  the  -f-  of  the  ball,  the  attrac- 

FIG.  143* 
tion  is  greater  than  the  repulsion.    If 

the  pith  ball  be  suspended,  not  by  a  silk  thread  but  by 
some  good  conductor,  the  attraction  will  be  more  marked, 
for  the  -f-  of  the  ball  will  escape  to  the  earth,  through  the 
support,  and  the  repelling  component  thus  removed. 

Note.— Polarization  and  electrification  by  induction  explain  a  host 
of  phenomena.  Let  the  pupil  apply  this  principle  of  influence  or 
induction  to  pointing  out  the  changes  in  the  positions  and  conditions 
of  the  two  fluids  that  are  involved  in  the  phenomena  mentioned  in 
§323. 

342.  The   Electrophorus. — This  simple  instru- 
ment consists  generally  of  a  shallow  tinned  pan  filled  with 

resin,  on  which  rests  a  movable 
metallic  cover  with  a  glass  or 
other  insulating  handle.  The 
resinous  plate  may  be  replaced 
by  a  piece  of  vulcanized  india- 
rubber.  The  metal  surface 
and  the  resinous  surface  touch 
at  only  a  few  points;  they  are 
practically  separated  by  a  thin 
layer  of  air.  (Appendix,  K.) 

(a.)  The  plate  is  rubbed  or  struck 
FIG.  144.  witk  flannel  or  catskin,  and  thus 


FRICTIONAL  ELECTRICITY. 


207 


negatively  electrified.  The  cover  is  then  placed  upon  the  resin 
and  thus  polarized  by  induction.  If  the  cover  be  provided  with 
a  gold-leaf  electroscope,  the  free  negative  electricity  of  the  cover 
will  cause  the  leaves  to  diverge  ;  the  positive  electricity  of  the 
cover  will  be  "bound"  on  the  under  side  of  the  cover  by  the 
attraction  of  the  negative  of  the  plate.  Remove  the  plate,  and 
the  separated  fluids  reunite  as  is  shown  by  the  falling  together 
of  the  lately  divergent  gold  leaves.  Place  the  cover  again  upon 
the  plate.  Polarization  is  manifested  by  the  divergence  of  the 
leaves.  Touch  the  cover  with  the  finger  as  shown  in  the  figure; 
the  free  —  electricity  escapes  and  the  leaves  fall.  The  cover  is  now 
charged  positively,  but  its  electricity  is  all  ''  bound "  at  the  under 
surface  of  the  plate,  and  cannot  cause  the  leaves  to  separate.  Re- 
move the  plate  by  its  insulating  handle,  and  the  electricity,  lately 
"  bound  "  but  now  "  free,"  diffuses  itself,  and  the  leaves  are  divergent 
with  +  electricity.  The  charged  cover  will  give  a  spark  to  the 
knuckle  or  other  unelectrified  body  presented  to  it.  (Fig.  145.) 

343.  The  Electrophorus  Charged  by  Induc- 
tion.— The  cover  may  be  thus  charged  and  discharged 
an  indefinite  number  of  times,  in  favorable  weather, 

•without  a  second  elec- 
trifying of  the  resinous 
plate.  This  could  not 
happen  if  the  electricity 
of  the  cover  were  drawn 
from  the  plate.  More- 
over, if  the  charge  of 
the  cover  were  drawn 
from  the  plate,  it  would 
be  — ,  and  not  -f. 
There  is  no  escape  from 
the  conclusion  that  the 
cover  is  charged  by  in- 
duction, and  not  by  con- 
duction. (See  Append- 
ix K.) 


FIG  145. 


208  FRICTIONAL  ELECTRICITY. 

(a.)  If  the  resin  were  a  good  conductor  like  the  metal  cover,  its 
molecules  would  all  receive  +  electricity  from  the  cover  and  give 
—  electricity  to  it.  But  as  the  resin  is  a  poor  conductor,  only  the 
very  few  molecules  that  come  into  actual  contact  with  the  cover  at 
each  charging  have  their  electrical  equilibrium  restored.  The  +  of 
the  cover  cannot  pass  through  them  to  their  electrified  neighbors. 
Hence  it  requires  a  great  many  placings  of  the  cover  upon  the  plate 
to  discharge  the  plate  by  reconveying  to  it  the  +  electricity  removed 
at  its  electrification.  When  the  cover  is  charged,  it  gives  up  part 
of  its  —  electricity  ;  when  it  is  discharged,  it  receives  this  —  elec- 
tricity back  again  from  the  body  which  discharges  it.  As  this 
giving  and  taking  is  neither  to  nor  from  the  resin,  it  may  be  con- 
tinued indefinitely.  A  Leyden  jar  (§  353)  may  be  charged  with  an 
electrophorus. 

344,  Effect  of  Pointed  Conductors. -^Before 
proceeding  to  study  the  electrical  machine  we  need  to 
understand  something  of  the  action  of  pointed  conduc- 
tors.    The  reason  of  this  action  we  shall  see  more  clearly 
as  we  proceed ;  but  the  action  itself,  viz.,  that  a  strong 
charge  of  electricity  will  easily  and  quietly  escape  from 
a  pointed  conductor,  is  clearly  shown  by  the  following 
experiments:    Place  a  carrot  horizontally  upon  an  insu- 
lating support.    Into  one  end  of  the  carrot  stick  a  sewing- 
needle.    Bring  the  electrified  glass  rod  near  the  point  of 
the  needle  without  touching  it.     The  —  electricity  of  the 
carrot  escapes  from  the  point  to  the  rod  and  the  carrot 
is  positively  charged.    And  now  for  another  experiment, 
not  so  easily  made,  but  still  certain  to  succeed  if  you  are 
careful.     Excite  the    glass  rod,  turn  the  needle  away 
from  it,  and  bring  the  rod  near  the  other  end  of  the 
carrot.     The  positive  electricity  is  now  repelled   to  the 
point  from  which  it  will  stream  into  the  air.     Remove 
the  rod  and  test  the  carrot ;  it  is  negatively  electrified. 

345.  The  Plate  Electric  Machine.— This  instrument  is 
represented  in  Fig.  146.    It  consists  of  an  insulator  (or  electric),  a 


PLATE  ELECTRIC  MACHINE. 


209 


rubber,  a  negative  and  a  prime  conductor.  The  electric  is  a  glass 
plate,  one,  two  or  three  feet  in  diameter.  This  plate  has  an  axis 
and  handle,  and  is  supported  upon  two  upright  columns.  The  rub- 


FIG.  146. 

ber  is  made  of  two  cushions  of  silk  or  leather,  covered  with  amal- 
gam. They  press  upon  the  sides  of  the  plate  and  are  supported 
from  the  negative  conductor,  with  which  they  are  in  electric  con- 
nection. The  negative  conductor,  JV,  is  supported  upon  an  insulat- 
ing column  and  placed  in  electrical  connection  with  the  earth  by 
means  of  a  chain  or  wire,  not  shown  in  the  figure.  The  prime 
conductor,  C,  is  supported  upon  an  insulating  column.  One  end  of 
the  prime  conductor  terminates  in  two  arms,  which  extend  one  on 
either  side  of  the  plate.  These  arms  being  studded  with  points 
projecting  toward  the  plate  are  called  combs.  The  teeth  of  the 
combs  are  not  shown  in  the  figure  ;  they  do  not  quite  touch  the  plate, 
A  silk  bag  is  often  supported  so  as  to  enclose  the  lower  part  of  the 
plate.  All  parts  of  the  instrument  except  the  teeth  of  the  combs 
are  carefully  rounded  and  polished,  sharp  points  and  edges  being 
avoided. 

346.  Operation  of  the  Plate  Machine.— The 

plate  is  turned  by  the  handle.  The  neutral  fluid  is  de- 
composed by  the  friction  of  the  rubbers.  The  -f  of  the 


210  DIELECTRIC  MACHINE. 

rubber  and  negative  conductor  passes  to  the  place ;  the  — 
of  the  plate  passes  to  the  rubber  and  negative  conductor. 
The  part  of  the  plate  thus  positively  charged  passes  to  the 
combs  of  the  prime  conductor,  being  protected  by  the  silk 
bag  from  discharge  (neutralization)  by  the  air  on  the  way. 
The  -f-  of  the  plate  acts  inductively  upon  the  prime 
conductor,  polarizes  it,  repels  the  +  and  attracts  the  — 
electricities.  Some  of  the  —  electricity  thus  attracted 
streams  from  the  points  of  the  combs  against  the  glass, 
while  some  of  the  +  of  the  glass  escapes  to  the  prime 
conductor.  This  neutralizes  that  part  of  the  plate,  or 
restores  its  electric  equilibrium,  and  leaves  the  prime  con- 
ductor positively  charged.  As  each  successive  part  of  the 
plate  passes  the  rubber  it  gives  off  —  electricity  and  takes 
an  equal  amount  of  +;  as  it  passes  between  the  combs  it 
gives  off  its  +  electricity  and  takes  an  equal  amount  of  — . 
The  rubber  and  negative  conductor  are  kept  in  equilibrium 
by  means  of  their  connection  with  the  earth,  the  common 
reservoir.  As  the  plate  revolves,  the  lower  part,  passing 
from  N  to  C,  is  positively  charged  ;  the  upper  part,  pass- 
ing from  C  to  Ny  is  neutralized.  If  negative  electricity  be 
desired,  the  ground  connection  is  changed  from  N  to  (7, 
and  the  charge  taken  from  N. 

347.  The  Dielectric  Machine.— This  instrument  is 
represented  in  Fig.  147.  Two  plates  of  vulcanite  (ebonite),  A  and 
B,  overlap  each  other  without  touching,  and  revolve  in  opposite 
directions.  The  upper  plate  is  made  to  revolve  much  more  rapidly 
than  the  lower  by  means  of  the  pulleys  shown  at  the  right  of  the 
figure.  The  prime  conductor  and  the  axes  of  the  two  plates  are  car- 
ried by  two  insulating  pillars.  From  the  prime  conductor  a  comb 
is  presented  to  the  upper  part  of  the  upper  plate.  Another  eomb 
is  presented  to  that  part  of  A  which  is  overlapped  by  the  upper 
part  of  B.  This  comb  is  connected  by  a  universal  joint  at  e  with  a 
discharging  rod  and  ball,  which  may  be  brought  near  the  end  of  the 


DIELECTRIC  MACHINE. 


211 


prime  conductor  or  turned  away  from  it.     The  rubbers  and  the 

lower  comb  are  to  be  in 
electrical  communication 
with  the  earth.  The  gene- 
ral arrangement  is  clearly 
set  forth  in  the  figure. 

348.  Operation 
of  the  Dielectric 
Machine. — The  plate 
B  is  turned  directly  by 
the  handle,  and  the  plate 
A  indirectly  by  the  aid 
of  the  pulley.  The  plate 
B  is  negatively  electri- 
fied by  friction  with  the 
rubber,  and  thus  acts 
by  induction  upon  the 
lower  part  of  A,  which 
is  thus  polarized.  The  -f  of  this  part  of  A  is  bound  by  the 
attraction  of  the  —  of  B,  while  the  —  of  A  is  repelled, 
escapes  by  the  lower  comb,  and  is  replaced  by  -f  from  the 
earth  through  the  lower  comb  and  its  ground  connection. 
This  part  of  A,  thus  positively  charged,  is  soon  removed 
from  the  inducing  body,  and  the  +  charge  bound  by  B  is 
set  free.  It  then  comes  to  the  upper  comb,  polarizes  it  and 
the  prime  conductor  by  induction,  exchanges  some  of  its 
own  +  for  an  equal  amount  of  —  from  the  prime  con- 
ductor. This  neutralizes  that  part  of  the  upper  plate,  and 
leaves  the  prime  conductor  positively  charged.  As  each 
successive  part  of  A  passes  the  lower  comb  it  gives  off  — 
electricity  and  takes  an  equal  amount  of  -f- ;  as  it  passes 
the  upper  comb  it  gives  off  -j-  electricity  and  receives  an 
equal  amount  of  — .  The  charge  of  B  is  continually 


FIG.  147. 


212 


HOLTZ  ELECTRIC  MACHINE. 


maintained  by  friction  with  the  rubber.  When  the  dis~ 
charging  rod  and  ball  are  brought  near  the  prime  con- 
ductor, as  shown  in  the  figure,  a  rapid  succession  of  sparks 
is  produced,  owing  to  the  recombination  of  the  separated 
electricities.  If  another  body  is  to  be  charged  from  the 
prime  conductor,  the  ball  and  rod  may  be  turned  aside. 
The  power  of  this  machine  is  greater  than  that  of  the  plate 
or  cylinder  ma- 
chine; it  is  less 
affected  by  at- 
mospheric moist- 
ure, and  is  more 
compact. 

349.      The 

Holtz    Electric 
Machine.— T  h  i  s 

instrument  is  repre- 
sented  in  Fig.  148. 

It  contains  two  thin  circular  plates  of  glass,  the  larger  of  which  is 
held  fast  by  two  fixed  pillars.  The  smaller  plate  revolves  rapidly 
very  near  it.  There  are  two  holes  in  the  fixed  plate  near  the 
extremities  of  its  horizontal  diameter.  To  the  sides  of  these  open- 
ings are  fastened  paper  bands  called  armatures.  Opposite  these 
armatures,  and  separated  from  them  by  the  revolving  plate,  are 
two  metallic  combs,  connected  respectively  with  the  two  knobs 
shown  in  the  front  of  the  picture.  One  of  these  knobs  is  carried 
by  a  sliding  rod  so  that  their  distance  apart  is  easily  adjusted.  In 
using  the  machine,  the  knobs  are  placed  in  contact,  one  of  the 
armatures  is  electrified  by  holding  against  it  an  electrified  sheet  of 
vulcanite,  the  handle  is  turned  for  a  few  seconds,  and  the  knobs 
gradually  separated.  A  series  of  electric  discharges  between  the 
two  knobs  takes  place.  When  this  machine  works  well,  it  gives 
results  superior  to  either  of  those  previously  mentioned.  It  is, 
however,  peculiarly  subject  to  atmospheric  conditions,  and  is  gen- 
erally considered  extremely  capricious. 


. — When  used,  any  electrical  machine  should  be  free  from 
dust  and  perfectly  dry.     It  should  be  warmer  than  the  atmosphere 


ELECTRIC  DENSITT.  213 

of  the  room,  tliat  it  may  not  condense  moisture  from  the  surrounding 
air.  The  dryer  the  atmosphere  the  better  will  be  the  action  of  the 
machine. 

35O.  Electric  Density  or  Tension. — We  already 
have  the  idea  that  all  bodies,  at  all  times  and  under  all 
conditions,  have  a  certain  quantity  of  the  electric  fluid. 
This  quantity  may  be  all  -f  or  all  — ,  or  partly  one  and 
partly  the  other,  the  +  and  —  mingling  in  all  propor- 
tions. The  kind  may  vary;  the  quantity  is  constant.  If 
this  quantity  be  equally  divided  between  the  +  and  the  — , 
the  body  is  unelectrified.  If  the  +  be  slightly  in  excess, 
the  body  is  feebly  charged  positively,  and  vice  versa.  If 
more  —  be  replaced  by  more  +,  the  positive  charge  is 
increased ;  that  is,  the  excess  of  the  positive  over  the  neg- 
ative is  increased.  This  excess  is  the  resultant  or  available 
force.  If  all  of  the  —  could  be  removed  and  an  equal 
amount  of  -f-  substituted  therefor,  the  resultant  would 
equal  the  total  constant  quantity  and  the  charge  would 
reach  the  theoretical  maximum.  What  we  call  electric 
density  or  tension  may  be  considered  the  value  of  this 
excess  of  either  fluid  over  its  opposite.  When  this  excess 
or  difference  is  great,  the  charge  is  said  to  be  powerful  or 
intense  ;  the  density  or  tension  is  great. 

QUESTIONS. 

1.  (a.)  Why  is  electricity  called  a  force  ?    (6.)  How  can  you  show 
that  it  is  a  force?    (c.)  Define  positive  electricity,    (d.)  Define  nega- 
tive electricity,    (e.)  How  can  you  show  that  there  are  two  opposite 
kinds  of  electricity  ? 

2.  («.)  How  would  you  test  the  kind  of  electricity  of  an  electri- 
fied body?    (&.)  Give  the  theory  of  two  electric  fluids. 

3.  (a.)  What  is  a  proof  plane?     (&.)  An  electroscope?     (c.)  De- 
scribe one  kind  of  electroscope,     (d.)  Another  kind. 

4.  (a.}  Define  electrics,  conductors  and  insulators.    (&.)  Show  the 


214  ELECTRIC  CONDEXSBRS. 

relation  of  the  first  of  these  to  each  of  the  others,     (c.)  Explain 
electric  induction. 

5.  (a. )  If  a  metal  globe  suspended  by  a  silk  cord  be  brought  near 
the  prime  conductor  of  an  electric  machine  in  action,  feeble  sparks 
will  be  produced.  Explain.  (&.)  If  the  globe  be  held  in  the  hand, 
stronger  sparks  will  be  produced.  Explain. 

Recapitulation.— In  this  section  we  have  considered 
Electric  Attraction  and  Repulsion ;  Electricity  as 
a  Force  ;  the  existence  of  Two  Kinds  of  Elec- 
tricity and  their  names;  the  Law  of  Electric  Action  ; 
Tests  for  the  presence  and  kind  of  Electricity;  Elec- 
troscopes and  their  use;  Conductors,  Insula- 
tors and  Electrics  ;  the  Theory  of  Electric  Fluids ; 
Electric  Induction;  Inductive  Electrification; 
that  Polarization  Precedes  Electric  attraction ; 
the  Electrophorus  ;  the  Plate  and  the  Dielectric 
machines  and  the  Operation  of  each ;  the  Holtz 
machine ;  Electric  Tension. 


ECTION  HI. 


ELECTRIC    CONDENSERS;    LIGHTNING;    EXPERI- 
MENTS. 

351.    Condensation    of   Electricity.— By   the 

words  condensation  of  electricity  we  mean  the  process  of 
increasing  the  charge  which  a  body  may  receive  from  an 
electrified  body  having  a  given  tension.  If  an  insulated 
conductor  be  brought  into  contact  with  the  charged  prime 
conductor  of  an  electric  machine,  the  intensity  of  the 
charge  received  cannot  exceed  that  of  the  prime  con- 


UNIVERSITY 


ELECTRIC  CONDENSERS. 


ductor,  for  obvious  reasons.    But  if  two  conducting  plates, 
A  and  B,  separated  by  a  non-conductor,  C,  be  connected 
c  with,  the  prime  conductor,  and 

the  plate,  A,  provided  with  a 
ground  connection,  as  shown 
in  Fig.  149,  the  charge  of  B 
will  be  more  intense  than  that 
of  the  prime  conductor;  its 
tension  will  be  greater  than 
that  of  the  charging  body.  If 
a  third  plate  like  B,  but  having 
V  :!::::  ,,..,.,.,::„,.  no  opposite  plate  like  A,  be 
Hi  connected  with  B  by  a  copper 
wire  and  the  middle  of  the  wire 
brought  into  contact  with  the 
prime  conductor,  nearly  the  whole  charge  will  go  to  B  and 
very  little  to  the  third  plate,  which  has  no  condenser  like  A. 


FIG.  149. 


352.  Electric  Condensers.  —  The  electric  condenser  is  a 
contrivance  by  which  the  tension 
of  the  body  charged  may  be  made 
greater  than  the  tension  of  the 
body  charging.  Let  A  and  B, 
Fig.  150,  represent  two  insulated 
metallic  plates  about  six  inches  in 
diameter,  separated  by  C,  a  plate 
of  glass  somewhat  larger.  Let 
each  metallic  plate  have  an  elec- 
tric pendulum,  a  and  b.  Remove 
A,  and  connect  B  with  the  con- 
ductor  of  the  electric  machine. 
The  divergence  of  b  shows  the  presence  of  free  electricity.  If  the 
wire  x  were  now  cut,  no  change  would  take  place.  Connect  A  with 
the  ground  by  the  wire  y,  and  place  in  position  as  represented.  By 
the  inductive  influence  of  B,  the  neutral  electricity  of  A  is  decom- 
posed, its  negative  electricity  being  drawn  to  the  surface  n,  while 
the  positive  escapes  by  y.  But  this  negative  electricity  at  n  attracts 
the  positive  of  B  largely  to  the  surface  m,  and  holds  it  there  as 


FIG.  150. 


CONDENSERS. 


FIG.  151. 


bound  electricity.  This  change  is  shown  by  less  divergence  of  &. 
Consequently  J3  can  receive  more  electricity  from  the  machine 
which  will  attract  more 
negative  electricity  to 
n.  This  further  sup- 
ply will  in  turn  bind 
more  of  the  positive 
electricity  of  B  at  m.  In 
this  way  a  large  quan- 
tity of  positive  elec- 
tricity may  be  accumu- 
lated at  m,  and  a  large 
quantity  of  negative  at 
n.  This  accumulation 
may  thus  go  on  until 
the  intensity  at  the 
surface,  p,  is  equal  to 
that  of  the  machine,  as 
it  was  when  A  was  absent.  Interrupting  communication  by  x  and  y, 
both  plates  are  charged.  The  vertical  pendulum  a  shows  no  free 
electricity,  the  electricity  of  A  being  all  bound  at  n  ;  the  pendulum 
at  6  shows  some  free  electricity,  although  the  greater  part  of  the 
electricity  of  B  is  bound  at  m.  Remove  A  and  B  from  each  other, 
and  the  bound  electricity  of  each  is  set  free,  and  both  a  and  b  are 
widely  divergent.  The  complete  apparatus  is  represented  by  Fig.  151. 

353.  The  Leydeii  Jar. — The  Leyden  jar  consists  of 
a  glass  jar  coated  within  and  without  for  about  two-thirds 
its  height  with  tinfoil.  The  mouth  of  the  jar  is  closed 
with  a  cork  through  which  passes  a  metallic  rod,  commu- 
nicating by  means  of  a  small  chain  with  the  inner 
coat  and  terminating  above  in  a  knob.  The  cork 
and  the  upper  part  of  the  jar  are  generally  coated 
with  sealing-wax  or  shellac  varnish  to  lessen  the 
deposition  of  moisture  from  the  air.  It  is  evi- 
dently a  modified  electric  condenser.  The  inner 
coat  represents  the  collecting  plate  B ;  the  glass 
jar,  the  insulator  plate  (7;  the  outer  coat  the 
FIG.  152.  condensing  plate  A  (Fig.  150). 


ELECTRIC   CONDENSERS.  217 

354.  Charging  the  Leycleii  Jar. — To  charge  the 
jar,  hold  it  in  the  hand  as  shown  in  Fig.  153,  and  bring 
the  knob  near  or  into  contact  with  the  prime  conductor  of 
an  electrical  machine  which  is  in  action. 

(a.)  The  prime  conductor  being  positively  charged  -attracts  the  — 
from  the  inner  coat  and  replaces  it  with  its  own  + .  This  +  charge 
of  the  inner  coat  acting  inductively  through  the  glass  polarizes  the 


I  i; 


FIG.  153. 

outer  coat,  repelling  the  +  which  escapes  through  the  hand  to  the 
earth,  and  binding  its  —  to  the  surface  in  contact  with  the  glass. 
This  bound  negative  electricity  of  the  outer  coat,  in  turn,  binds  the 
positive  of  the  inner  coat,  and  so  on.  If,  instead  of  holding  the 
outer  coat  in  the  hand,  the  jar  be  supported  upon  a  pane  of  glass  so 
that  the  repelled  electricity  of  the  outer  coat  cannot  escape,  the  jar 
cannot  be  very  intensely  charged. 

355.  Discharging  the  Leyden  Jar.— The  jar 
might  be  discharged  by  touching  the  knob  with  the  finger, 
the  separated  electricities  coming  together  through  the 
person  of  the  experimenter  and  the  earth.  In  this  case  the 
experimenter  will  feel  a  "  shock."  If  the  charge  bo  intense, 

the  shock  will  be  painful  or 
even  dangerous.  It  is  better 
to  use  a  "discharger,"  two 
forms  of  which  are  represented 
in  Fig.  154.  This  consists 
of  two  metal  arms  hinged 
FIG.  154.  together,  carrying  knobs  at 

10 


218 


ELECTRIC   CONDENSERS. 


their  free  ends  and  carried  by  insulating  handles, 
outer  coat  should  be  touched  first.    Why  ? 


The 


356.  The  Leyclen  Jar  with  Movable  Coats.— This 
piece  of  apparatus  is  represented  by  Fig.  155.    The  three  parts  being 
placed  together  in  proper  order,  B  within  A  and  C  within  B,  the 
jar  is  charged  in  the  usual  manner.     The  inner  coat  C  is  then 
removed  with  a  glass  rod  and  touched  with  the  hand  to  discharge  it 
fully.    B  is  then  lifted  out  from  A  and  the  outer  coat  fully  dis- 
charged.    The  three  parts  are  then  put  together  again  and  found  to 
be  able  to  give  nearly  as  strong  a  spark  as  at  first.     This  seems  to 
indicate  that  the  charge  rests  upon  the  sur- 
faces of  the  glass  rather  than  upon  the  sur- 
faces of  the  coats.    If  when  the  charged  jar  is 

in  pieces,  the  thumb  be  placed  on  the  outer 
surface  of  the  glass  and  the  forefinger  of  the 
same  hand  on  the  inner  surface,  a  very  slight 
shock  is  perceptible.  The  oppositely  charged 
glass  molecules  that  come  into  actual  contact 
with  thumb  and  finger  respectively  are  dis- 
charged. By  changing  the  position  of  the 
thumb  and  finger,  successive  little  shocks 
may  be  felt  as  successive  portions  of  the 
inner  and  outer  surfaces  of  the  glass  are  dis- 
charged. The  inner  coat  furnishes  a  means 
for  the  simultaneous  discharge  of  the  inner 
layer  of  glass  molecules  ;  the  outer  coat  does 
the  same  for  the  outer  layer  of  glass  mole- 
cules. Thus  all  or  nearly  all  of  the  electrified  ^ 
glass  molecules  may  be  discharged  simul-  f 
taneously  instead  of  successively.  P 

357.  The  Leyden  Battery.— The  effect  that  may 
be  produced  with  a  Leyden  jar  depends  upon  its  size  and 
the  thinness  of  the  glass.    But  a  large  jar  is  expensive  and 
requires  great  care;  thin  glass  is  liable  to  perforation  by 
the  condensed  and  strongly  attracting  electricities  of  its 
two  coats.    To  obviate  both  of  these  difficulties  a  collection 
of  jars  is  used.     When  their  outer  coats  are  in  electric  com- 
munication, which  may  be  secured  by  placing  them  in  a 


ELECTRIC   CONDENSERS. 


219 


tray,  the  bottom  of  which  is  covered  with  tinfoil,  and  their 
inner  coats  are  connected  by  wires  or  metal  strips  passing 


FIG.  156. 

from  rod  to  rod,  or  from  knob  to  knob,  the  apparatus 
is  called  a  Leyden  or  electric   battery.     The  battery  is 


FIG.  15,. 


220 


ELECTRIC  CONDENSERS. 


charged  and  discharged  in  the  same  way  as  a  single  jar ; 
but  great  care  is  needed,  for  if  the  discharge  were  to  take 
place  through  the  human  body  the  result  would  be  serious 
and  possibly  fatal. 

358.  Distribution  of  Electricity.— Many  ex- 
periments have  been  made  which  go  to  show  that  when  a 
body  is  electrified,  the  electricity  passes  to  the  surface  and 
escapes  if  the  body  be  not  insulated.  A  bomb-shell  and  a 
cannon-ball  of  equal  size  will  receive  equal  quantities  of 
electricity  from  the  same  source.  The  hollow  conductors 
used  in  electric  experiments  are  as  serviceable  as  if  they 
were  solid. 


FIG.  158. 

(a.)  A  metal  globe  with  an  insulating  support  (Fig.  157)  is  pro- 
vided with  two  closely-fitting  hemispherical  shells  having  insulating 


ELECTRIC  DISTRIBUTION.  221 

handles.  Electrify  the  globe  ;  bring  it  near  the  electroscope  to  be 
sure  that  it  is  electrified.  Place  the  hemispheres  upon  the  globe. 
Remove  them  quickly,  being  careful  that  their  edges  do  not  touch 
the  sphere  after  the  first  separation.  Bring  first  one  shell  and  then 
the  other  near  the  electroscope  ;  they  are  electrified.  Bring  the 
globe  itself  near  the  electroscope.  It  is  no  longer  electrified.  Delicate 
manipulation  is  needed  to  make  the  experiment  successful.  You 
will  fail,  perhaps,  more  times  than  you  succeed.  But  when  the 
experiment  is  successful,  it  is  instructive.  The  apparatus  is  called 
Biot's  hemispheres. 

(6.)  Charge  with  electricity  a  hollow  sphere  having  an  orifice  in 
the  top.  Bring  a  proof-plane,  made  by  fastening  a  disc  of  gilt  pat>er 
to  a  long  thin  insulating  handle,  into  contact  with  the  outer  surface 
of  the  sphere.  The  proof  plane  is  charged  by  the  sphere,  as  may  be 
shown  by  bringing  it  near  an  electroscope.  Discharge  the  proof - 
Diane  and  bring  it  into  contact  with  the  inner  surface  of  the  sphere. 
Remove  it  carefully  without  allowing  it  to  touch  the  sides  of  the 
orifice.  Bring  it  to  the  electroscope.  It  is  not  charged.  (Fig.  158.) 

(c.)  Vary  the  experiment  by  the  use 
of  Faraday's  bag.  This  consists  of  a 
conical  bag  of  linen,  supported,  as 
shown  in  Fig.  159,  by  an  insulated  metal 
hoop  five  or  six  inches  in  diameter.  A 
long  silk  thread  extending  each  way 
from  the  apex  of  the  cone  enables  the 
experimenter  to  turn  the  bag  inside- 
out  without  discharging  it.  Whichever 
surface  of  the  linen  is  external,  no  elec- 
tricity can  be  found  upon  the  inside  of 
the  bag.  Nothing  can  be  more  conclu- 
sive than  this. 

(d.)  Vary  the  experiment  by  the  use  pIG.  159. 

of  a   hat  suspended    by  silk  threads. 

Notice  that  the  greatest  charge  can  be  obtained  from  the  edges  ; 
less  from  the  curved  or  flat  surface  ;  none  from  the  inside. 

Note. — This  rule  does  not  apply  to  an  electric  current.  A  hollow 
wire  will  not  conduct  electricity  as  well  as  a  solid  wire  of  the  same 
diameter.  Electricity  may  be  drawn  to  the  inside  of  a  hollow  con- 
ductor by  placing  there  an  insulated  body  oppositely  charged. 

359.  Distribution  of  Electricity  on  the 
Surface. — Experiments  show  that  when  a  sphere  is 
charged,  the  electricity  is  evenly  distributed  over  the  sur- 


ATMOSPHERIC  ELECTRICITY. 

face.  Similar  experiments  on  an  elongated  cylinder,  like 
the  prime  conductor  of  the  electric  machine,  show  that 
the  density  is  greater  at  the  ends.  On  an  ovoid  conductor, 
like  that  shown  in  Fig.  160,  the  density  is 
greatest  at  the  smaller  end.  In  general,  the 
electric  density  is  greatest  on  those  parts  of 
a  charged  conductor  which  project  the  most 
and  have  the  sharpest  ends.  This  tension 
at  a  point  may  become  so  great  that  the 
FIG.  160.  electricity  will  escape  rapidly  and  quietly. 
This  explains  the  action  of  points,  which  plays  so  impor- 
tant a  part  in  the  action  of  electric  machines.  This 
property  will  he  illustrated  in  several  of  the  experiments 
in  §  371.  It  is  also  fundamental  to  the  action  of  lightning- 
rods. 

360.  Atmospheric  Electricity.— The  identity  of 
lightning  with  electricity,  though  long  suspected,  was  first 
proved  by  Franklin's  famous  kite  experiment.     The  at- 
mosphere is,  at  all  times,  more  or  less  electrified.     The 
kind  and  intensity  of  this  atmospheric  electricity  varies  at 
different  times.     In  fair  weather,  the  atmospheric  elec- 
tricity is  generally  positive.   The  friction  of  moving  masses 
of  air  probably  contributes  to  the  presence  of  atmospheric 
electricity. 

361.  Electrified  Clouds. — Dry  air  being  a  poor 
electric  conductor    (§  333),    the  air  particles  discharge 
their  electricity  into  each  other  slowly  and  with  difficulty. 
The  electricity  thus  prevented   from  accumulating  has 
little  density  or  tension,  and  hence  gives  few  manifestations 
of  its  presence.     The  moist  particles  which  constitute  a 
cloud  being  good  conductors,  the  atmospheric  electricity 


LIGHTNING.  223 

involved  in  the  cloud  is  quickly  discharged  from  one 
particle  to  another,  and  accumulates  on  the  surface  of 
the  cloud  (§  358).  A  cloud  may  thus  become  intensely 
charged.  The  charge  is  generally  positive. 

362,  Lightning. — When  a  cloud  positively  charged 
floats  over  the  earth,  separated  from  it  by  a  layer  of 
insulating  air,  the  inductive  influence  of  the  cloud  ren- 
ders the  ground  beneath  negatively  electrified.     Then  the 
cloud,  ground,  and  insulating  air,  correspond  respectively 
to  the  inner  and  outer  coatings  and  the  insulating  glass 
of  a  Leyden  jar.    As  the  charge  of  a  Leyden  jar  may  be 
made  so  intense  that  the  mutual  attraction  of  the  sepa- 
rated electricities  will  result  in  their  rushing  together  and 
thus  piercing  the  jar  (§  357),  so  the  charge  of  a  cloud 
may  become  sufficiently  intense  to  overcome  the  inter- 
vening resistance  and  a  lightning  stroke  ensues.     Two 
clouds  charged  with  opposite  electricities  may  float  near 
each  other.     Then  they,  with  the  intervening  air,  may  be 
looked  upon  as  constituting  a  huge  Leyden  jar.     Thus  we 
may  see  the  lightning  leaping  from  cloud  to  earth,  or 
from  cloud  to  cloud. 

363.  Lightning-Rods.— The  value  of  lightning- 
rods  depends  upon  the  tendency  of  electricity  to  follow 
the  best  conductor,  and  upon  the  effect  of  pointed  con- 
ductors upon  electrical  intensity  (§  359).     The  lightning- 
rod  should,   therefore,   be   made  of   a  good  conductor; 
copper  is  better  than  iron.     It  should  terminate  above  in 
one  or  more  points,  tipped  with  some  substance  that  may 
be  corroded  or  fused  only  with  extreme  difficulty.     Plati- 
num is  a  metal  which  satisfies  these  conditions  very  well. 
The  rod  should  extend  above  the  highest  point  of  the 


224  VELOCITY  OF  ELECTRICITY. 

building  in  order  to  offer  the  electricity  the  shortest  path 
to  the  ground.  It  is  important  to  have  each  projecting 
part  of  the  building,  as  chimneys,  towers  and  gables,  pro- 
tected by  a  separate  rod.  The  rod  should  afford  an  un- 
broken connection ;  the  joints,  if  there  be  any,  should  be 
carefully  made.  The  rod  should  terminate  below  in  water, 
or  in  earth  that  is  always  moist.  A  rod  having  a  blunted 
tip,  a  broken  joint,  or  terminating  in  dry  earth,  is  more 
dangerous  than  no  rod  at  all. 

(a.)  The  greatest  value  of  a  lightning-rod  is  due  to  its  quiet  work 
in  the  prevention  of  the  lightning  stroke.  Bring  the  point  of  a  knife- 
blade  near  the  conductor  of  an  electric  machine  in  operation,  and 
notice  the  instant  cessation  of  sparks.  The  quiet  passage  of  elec- 
tricity from  the  earth  neutralizes  the  charge  of  the  conductor  and 
restores  the  electric  equilibrium.  In  the  same  way,  a  lightning-rod 
tends  to  restore  the  electric  equilibrium  of  the  cloud,  a -id  prevent 
the  dangerous  discharge.  For  this  quiet  but  very  valuable  service, 
few  persons  ever  give  the  rod  any  credit.  Every  leaf  of  the  forest 
and  every  blade  of  grass  is  a  pointed  conductor  acting  in  the  same 
way.  (§371  [9].) 

364.  Velocity  of  Electricity  and  Duration 

of  the  Spark.— Experiment  has  shown  that  the 
velocity  of  electricity  along  an  insulated  copper  wire  is 
about  288,000  miles  per  second,  and  that  the  duration  of 
the  electric  spark  is  not  more  than  -^Q-Q  of  a  second. 
The  danger  from  any  lightning  stroke  has  passed  when  we 
hear  the  crash.  (§  425.) 

365.  Thermal  Effects. — When  an  electric  current 
has  to  overcome  a  resistance  in  its  passage,  heat  is  pro- 
duced.    By  passing  a  strong  current  over  a  small  wire,  the 
wire  may  be  heated  to  fusion.     Metals  have   even  been 
vaporized  by  electricity.     The  worse  conductor  a  wire  is, 
the  more  it  is  heated.    See  §  371,  [19]-[23].     By  means 
of  a  Leyden  battery  and  a  universal  discharger,  remark- 


ELECTRIC  EFFECTS.  225 

able  thermal  effects  may  be  obtained.    Houses  are  some- 
times set  on  fire  by  lightning. 

366.  Luminous  Effects. — The  luminous  effects  of 
electricity  are  due  to  discharges  through  bad  conductors. 
The  electric  spark  is  the  most  familiar  example.     The 
glow  seen  when  electricity  escapes  from  a  pointed  con- 
ductor in  the  dark,  and  the  various  forms  of  lightning, 
render  familiar  the  luminous  effects  of  electricity.     (§  371, 
[24H31]). 

367.  Magnetic  Effects.— A  common  needle  may 
be  magnetized  by  winding  about  it  a  covered  copper  wire 
and  discharging  a  Leyden  jar  through  the  wire.     The 
magnetic  effects  of  electricity  are  better  and  more  com- 
monly shown  with  Voltaic  electricity.     (§  392.) 

368.  Chemical  Effects. — The  electric  spark  may 
be  made  to  produce  chemical  combination   or  chemical 
decomposition.     Ammonia  gas  (NH3),   or  carbonic  acid 
gas  (C02),  may  be  decomposed  by  passing  a  series  of  sparks 
through  it.     A  mixture  of  oxygen  and  hydrogen  may  be 
caused  to  enter  into  chemical  union  by  the  electric  spark, 
the  product  of  the  union  being  water  (H20).  (§  371  [35].) 

369.  Mechanical  Effects.— The  piercing  of  the 
glass  walls  of  an  overcharged  Leyden  jar  affords  a  good, 
though  expensive,  illustration  of  the  mechanical  effects  of 
electricity.     Trees  and  telegraph  poles  shattered  by  light- 
ning are  not  unfamiliar.     (§  371  [32]-[34].) 

(a.)  Charge  a  Leyden  jar.  In  discharging  it,  hold  a  stiff  card 
between  the  knob  of  the  jar  and  the  knob  of  the  discharger.  A 
hole  will  be  pierced  through  the  card.  By  the  side  of  this  hole  in 
the  card  make  another  with  a  pin.  Any  one  can  tell  by  examina- 
tion of  the  pin  hole  from  which  side  of  the  card  it  was  pierced  ;  it 
is  burred  on  only  one  side.  Not  so  with  the  perforation  made  by 


226 


ELECTRIC  EFFECTS. 


electricity  ;  it  is  burred  on  both  sides.    The  phenomena  of  attraction 
and  repulsion,  already  made  familiar,  come  under  this  head. 

370.  Physiological    Effects.  — The    "electric 
shock,"  which  is  physiological  in  its  nature,  is  familiar  to 
most  persons.     The  sensation  thus  produced  cannot  be 
described,  forgotten  or  produced  by  any  other  agency.     It 
has  been  found  an  efficient  agent  in   medical  practice. 
Such  experiments,   however,  should  be  performed  with 
caution. 

(a.)  If  the  members  of  a  class  form  a  chain  by  joining  hands,  the 
first  member  holding  a  feebly-charged  Leyden  jar  by  its  outer  coat, 
and  the  last  member  touching  the  knob,  a  simultaneous  shock  will 
be  felt  by  each  person  in  the  chain.  A  single  Leyden  jar  has  thus 
been  discharged  through  a  regiment  of  1500  men,  each  soldier 
receiving  a  shock.  Dr.  Priestley  killed  a  rat  with  a  battery  of  seven 
feet  of  coated  surface,  and  a  cat  with  a  battery  of  forty  feet  of 
coated  surface. 

371.  Apparatus  and  Experiments.— It  is  not 

necessary  nor  very  desirable  that  all  of  the 
following  experiments  be  performed.  Several 
of  them  involve  the  same  principle ;  but  one 
teacher  may  have  one  piece  of  apparatus  and 
another,  another  piece. 


FIG.  161. 


(1.)  Fig.  161  repre- 
sents the  "electric 
bells."  The  metal 
frame  is  hung  from 
the  prime  conductor.  The  right-hand 
bell  is  suspended  by  a  wire  ;  the  other 
bell  is  suspended  by  a  silk  cord  and 
connected  with  the  ground  by  means 
of  a  chain  hanging  on  the  floor.  When 
the  machine  is  worked  slowly,  the 
clapper  vibrates  and  rings  the  bells. 
Explain. 

(2.)  In  the  "electric  chime,"  repre- 
sented   in    Fig.  162,  the    outer   bells 


FIG.  162. 


ELECTRIC  EXPERIMENTS. 


227 


FIG.  163. 


are  to  be  put  into  communication  with  the 
prime  conductor ;  the  larger  central  bell  is 
in  communication  with  the  earth.  The  clap- 
pers are  suspended  by  silk  threads.  When 
the  machine  is  slowly  worked,  the  bells  begin 
to  ring.  Explain. 

(8.)  In  the  "Leyden  jar  and  bells,"  shown 
in  Fig.  163,  the  left-hand  bell  is  in  communi- 
cation with  the  outer  coat  of  the  jar  ;  the  clap- 
per is  suspended  by  a  silk  thread.  When  the 
jar  is  charged  and  placed  in  position  as  repre- 
sented, the  bells  begin  to  ring  and  continue  to 
do  so  for  a  considerable  time.  Explain. 


(4.)  The  " metallic  plates  and  dancing  images"  are 
represented  in  Fig.  164.  The  images  are  made  of  pith. 
The  upper  plate  is  in  communication  with  the  prime 
conductor  ;  the  lower  one  with  the  earth.  When  the 
machine  is  worked,  the  images  dance  in  a  very  ludi- 
crous manner.  Explain.  Pith  balls  may  be  substi- 
tuted for  the  images,  the  resulting  phenomena  being 
known  as  "  Volta's  hail."  The  experiment  may  be 
simplified  by  electrifying  the  inner  surface  of  a  glass 
tumbler  by  rubbing  it  upon  the  knob  of  the  prime 
conductor,  and  placing  the  tumbler  over  some  pith 
balls  on  the  table. 


FIG.  164. 


FIG.  165. 


(5.)  In  the  "  electric  swing,"  shown  in  Fig.  165, 
the  boy  is  suspended  by  silk  cords.  One  of  the 
insulated  knobs  is  in  communication  with  the 
earth  ;  the  other  with  the  prime  conductor. 
When  the  machine  is  worked,  the  boy  swings  to 
and  fro.  Explain. 

(6.)  Electrify  a  glass  rod.    Toss  a  small  sheet 
of  gold  leaf  into  the  air.    Bring  the  rod  near  the 
leaf.     The  leaf  is  drawn  toward  the  rod  and  then 
thrown  off.     Chase  the  leaf  with  the  rod  without  letting  it  touch 
the  ground.     Explain. 

(7.)  Fasten  one  end  of  a  long,  small  copper  wire  to  the  prime 
conductor.  Near  the  other  end  of  the  wire,  tie  a  silk  cord  and  hang 
it  from  the  ceiling  or  other  support  so  that  the  end  of  the  vertical 
part  of  the  wire  shall  be  at  a  convenient  height.  To  this  end  of  the 
wire  attach  a  tassel  about  four  or  five  inches  long  made  of  many 
strips  of  light  tissue  paper.  Work  the  machine  and  the  leaves  will 


ELECTRIC  EXPERIMENTS. 


FIG.  166. 


diverge.  Explain.  Extend  toward  it  your  clenched  fist ;  the  leaves 
seek  the  fist.  Explain.  Instead  of  your  fist,  hold  a  needle  toward 
the  tassel ;  it  will  be  blown  away.  Explain.  Hold  the  needle 
upright  under  the  tassel.  The  strips  will  collapse.  Explain. 

(8.)  If  the  prime  conductor 
be  provided  with  a  point, 
the  flame  of  a  candle  held 
near  will  be  blown  away  as 
shown  in  Fig.  166.  If  the 
candle  be  placed  upon  the 
prime  conductor  and  a 
pointed  conductor  be  held 
in  the  hand  near  the  candle, 
the  flame  will  be  still  blown 
away.  Explain. 

(9.)  Stand  upon  the  insu- 
lating stool  and  place  your 
left  hand  upon  the  prime 
conductor  of  the  electric  ma- 
chine. Hold  in  your  right  hand  a  sewing-needle  with  the  tip  of  the 
forefinger  covering  the  end  of  the  needle.  Bring  the  right  hand 
cautiously  near  the  gold-leaf  electroscope.  Notice  the  divergence 
of  the  leaves.  Now  uncover  the  point  of  the  needle  and  bring  it 
near  the  electroscope.  Notice  the  marked  and  immediate  increase 
in  the  divergence  of  the  leaves.  Explain. 

(10.)  Place  an  "electric  whirl"  (which  consists  of  a  set 
of  horizontal  wire  arms  radiating  from  a  pivot-supported 
centre,  the  pointed  ends  being  all  bent  in  the  same  direc- 
tion) upon  the  prime  conductor.  Work  the  machine  and 
the  arms  will  revolve.  (See  Fig.  167.)  Explain. 

(11.)  The  "  electric  orrery,"  represented  in  Fig.  168,  is  a 
pretty  modification  of  the   "electric  whirl."    The  short  FIG.  167. 
balanced  bar  is  provided  with  a  pointed  conductor  to  pro- 
duce  rotary  motion  upon   its  supporting 
pivot,  which  is  one  end  of  the  long  balanced 
bar.     This  longer  bar  is  also  provided  with 
a  pointed  conductor  and  supported  in  turn 
upon  a  pivot,  which  may  be  attached  to  the 
prime  conductor.    When  the  machine  is 
worked,  the  long  bar  revolves  upon  its  fixed 
pivot ;    the    short   bar  revolves  upon  its 
FIG.  168,  moving  pivot. 


ELECTRIC  EXPERIMENTS.  229 

(12.)  If  a  pupil,  standing  upon  an  insulating  stool  (a  board  sup- 
ported by  four  warm  tumblers  will  answer)  and  having  one  hand 
upon  the  prime  conductor  of  an  electric  machine  in  action,  bring  a 
knuckle  of  the  other  hand  near  one  end  of  the  balanced  meter  stick 
(§  323),  it  will  follow  the  knuckle.  Explain. 

(13.)  If,  instead  of  placing  one  hand  upon  the  prime  conductor,  he 
hold  a  Leyden  jar  by  the  outer  coat  and  by  a  wire  connect  the  knob 
of  the  jar  with  the  prime  conductor,  his  knuckle  will  attract  the 
balanced  meter  stick  when  the  machine  is  worked.  Explain. 

(14.)  Half  fill  a  wide  glass  vessel  with  water.  Within  this  place 
a  glass  beaker  and  fill  this  to  the  same  level  with  water.  By  a 
wire,  connect  the  water  in  the  outer  vessel  with  the  earth  ;  in 
similar  manner  connect  the  water  in  the  beaker  with  the  electric 
machine.  Give  the  handle  of  the  machine  a  single  turn.  Dipping 
one  finger  into  the  outer  water  and  another  into  the  inner  water,  a 
shock  is  felt.  Explain. 

(15.)  Coat  both  sides  of  a  pane  of  glass  with  tinfoil  to  within  three 
inches  of  the  edge.  Place  the  under  coat  in,  communication  with 
the  ground  and  the  upper  coat  with  the  prime  conductor.  Place  a 
coin  upon  the  upper  coat  and  work  the  machine.  Try  to  remove 
the  coin  and  a  shock  will  be  felt.  Explain. 

(16.)  Let  a  pupil  stand  upon  an  insulating  stool  and  place  his  left 
hand  upon  the  prime  conductor.  Let  him  with  his  right  hand  clasp 
the  left  hand  of  another  pupil  not  insulated,  their  hands  being  pre- 
vented from  actual  contact  by  an  intervening  sheet  of  india-rubber 
cloth.  After  the  machine  has  been  worked  a  moment,  let  the  insu- 
lated pupil  remove  his  left  hand  from  the  prime  conductor  and  clasp 
the  free  hand  of  his  companion.  At  this  moment  of  clasping  hands 
a  shock  will  be  felt.  Explain. 

(17.)  Fasten  a  small  paper  kite  by  a  linen  thread  to  the  prime 
conductor.  When  the  machine  is  worked,  the  kite^will  float  around 
the  knob.  Explain. 

(18.)  Place  a  few  bits  of  paper  upon  the  cover  of  the  electropho- 
rus.  When  the  cover  has  been  touched  with  the  finger  and  lifted 
by  the  insulating  handle,  the  paper  will  be  thrown  off.  Explain. 

(19.)  Cover  one  knob  of  the  discharger  with  gun  cotton  sprinkled 
with  powdered  rosin.  When  the  Ley  den  jar  is  discharged  with 
this  discharger,  the  cotton  and  rosin  are  ignited. 

(20.)  The  "  electric  bomb,"  represented  in  Fig.  1G9,  may  be  made 
of  ivory,  heavy  glass,  or  thoroughly-seasoned  wood.  The  ends  of 
the  two  metal  wires  are  rounded  and  placed  a  short  distance  apart. 


230 


ELECTRIC  EXPERIMENTS. 


The  bomb  may  be  filled  with  gunpowder.    One  wire  is  connected 

by  a  chain  with  the  outer 

coat  of  a  charged  Leyden 

jar.    The  other  wire  is  to 

be    connected  with   the 

inner  coat  by  a  wet  string 

and  the  discharger.    The 


FIG.  169. 

spark  between  the  ends 
of  the  two  wires  ignites 
the  powder.  Try  the  ex- 
periment with  air  instead 
of  powder. 

(21.)    Fig.    170    illus-  FIG.  170. 

trates  a  method  of  igniting  an  inflammable  liquid,  like  ether  or 
alcohol,  by  the  electric  spark.  Through  the  bottom  of  a  small  glass 
vessel,  a,  passes  a  metal  rod,  having  a  knob  at  its  upper  extremity. 
The  lower  end  of  this  rod  may  be  brought  into  electrical  connection 
with  the  outer  coat  of  a  Leyden  jar.  Enough  ether  or  alcohol  is 
poured  into  a  just  to  cover  the  knob.  When  the  jar  is  discharged 
in  the  way  showai  in  the  figure,  the  spark  ignites  the  liquid.  If 
alcohol  is  used  it  may  have  to  be  warmed  to  render  the  experiment 
successful. 

(22.)  Let  a  pupil,  standing  on  an  insulating  stool,  become  charged 
by  holding  one  hand  on  the  prime  conductor  when  the  machine  is 
in  operation.  If  he  then  bring  his  knuckle  to  a  metal  burner  from 
which  a  jet  of  gas  is  issuing,  a  spark  will  pass  between  the  knuckle 
and  the  burner,  igniting  the  gas.  An  Argand  or  Bunsen  burner 
answers  well  for  this  experiment.  The  experiment  may  be  modi- 
fied by  using,  instead  of  the  knuckle,  an  icicle  held  in  the  hand. 

(23.)  The  "  universal  discharger,"  shown  in  Fig.  171,  consists  of  a 
glass  table  and  two  insulated  metal  rods.  The  rods  are  provided 


ELECTRIC  EXPERIMENTS. 


231 


with  balls,  points  and  pincers.  They  are  supported  upon  sliding 
and  hinged  joints,  so  that  they  may  be  easily  placed  in  any  desirable 
position.  If  the  adjacent  ends  of  the  two  rods  be  fitted  with  ball 
terminations  placed  upon  the  glass  table,  a  small  distance  apart,  a 
fine  wire  may  be  laid  from  one  to  the  other.  One  of  the  rods  may- 
be connected  by  a  wire  or  chain 
with  the  outer  coats  of  a  pow- 
erful battery ;  the  other  rod 
may  be  connected  by  the  dis- 
charger (Fig.  154)  with  the  inner 
coats  of  the  battery.  The  cur- 
rent thus  passed  along  the  fine 
wire  may  heat  it  to  incandes-  p. 

cence,  melt  or  even  vaporize  it. 

(24.)  One  of  the  inevitable  experiments  with  an  electric  machine 
consists  in  "drawing  sparks"  from  the  conductor  by  the  hand. 
When  the  tension  of  the  separated  electricities  becomes  sufficient 
to  overcome  the  resistance  of  the  intervening  air,  they  recombine 
with  a  sharp  explosive  sound  and  brilliant  flash  of  light.  If  the 


FIG.  172. 


ELECTRIC  EXPERIMENTS. 


length  of  the  spark  be  not  great,  the  spark  will  be  straight ;  if  it 
be  made  somewhat  greater,  it  takes  a  sinuous  and  forked  form,  as 
though  floating  dust  particles  served  as  stepping-stones  and  rendered 
a  crooked  path  the  easiest.  If  the  charge  be  very  powerful,  the 
spark  will  take  the  zigzag  form  so  familiar  in  the  lightning-stroke. 
In  the  dark,  the  continuous  discharge  into  the  air  produces  a 
luminous  appearance  at  the  ends  of  the  conductor.  This  appear- 
ance, known  as  a  brush,  may  be  im- 
proved by  holding  a  large,  smooth, 
metal  globe  at  a  distance  a  little  too 
great  for  the  passage  of  a  spark.  If 
the  conductor  be  provided  .with  a  point, 
the  point  will  glow  when  the  machine 
is  worked  in  the  dark. 

(25.)  Divide  a  circle  into  black  and 
white  sectors,  as  shown  in  Fig.  173,  and 
attach  it  to  a  whirling  table  (§   74). 
Revolve  it  so  rapidly  that  the  colors 
FIG.  173.  blend  and  the  disc  appears  a  uniform 

gray.     Darken  the  room  and  illuminate 

the  rapidly  revolving  disc  by  the  electric  spark  from  a  Ley  den  jar. 
The  disc  will  appear  at  rest,  and  each  sector  will  appear  separate 
from  its  neighbors.  This  shows  that  the  duration  of  the  electric 
spark  is  less  than  the  persistence  of  vision. 

(26.)  In  a  dark  room,  place  a  piece  of  loaf  sugar  in  contact  with 
the  outside  coat  of  a  charged  Leyden  jar.  Place 
one  knob  of  the  discharger  upon  the  sugar,  and 
bring  the  other  near  the  knob  of  the  jar.  When 
the  jar  is  discharged  thus  through  the  sugar,  the 
sugar  will  glow  for  some  time. 

(27.)  The  "  luminous  jar,"  represented  in  Fig.  174, 
is  a  modified  Leyden  jar.  The  outer  coat  consists 
chiefly  of  a  layer  of  varnish  sprinkled  over  with 
metallic  powder.  A  strip  of  tinfoil  at  the  bottom 
affords  means  of  communication  with  the  earth.  A 
similar  band  at  the  upper  edge  of  the  outer  coat  is 
provided  with  an  arm,  as  shown  in  the  figure.  The 
rod  of  the  jar  is  curved  so  as  to  bring  the  knob  near 
the  projecting  arm  of  the  outer  coat.  The  jar  13 
suspended  by  the  curved  rod  from  the  prime  conduc-  FIG.  174. 
tor,  and  its  lower  strip  of  tinfoil  connected  with  the 
earth.  When  the  machine  is  worked,  sparks  pass  between  the 
knob  and  the  projecting  arm.  In  a  dark  room,  the  metallic  powder 


ELECTRIC  EXPERIMENTS. 


333 


coat  will  be  beautifully  illuminated  at 
the  passage  of  each  such  spark. 

(28.)  The  "luminous  pane"  is  repre- 
sented in  Fig.  175.  A  continuous  tin- 
foil strip  is  pasted  back  and  forth  upon 
the  surface  of  a  plate  of  glass.  The 
upper  end  of  this  strip  is  connected  with 
the  prime  conductor  ;  the  lower  end 
with  the  earth.  A  series  of  breaks  in 
this  continuous  conductor  may  be  made 

by  cutting  it 

across  with  a 

sharp       pen- 
knife.  When 

the    machine 

is   worked    a 

small     spark 

will     appear 

at  each  break 

thus      made.  FIG.  175. 

These  breaks 

may  be  arranged  so   as  to  represent  a 

flower,      star,     arch, 

word  or  other  design. 

The  sparks  are  really 

successive,   but   they 

seem   to  be  simulta- 
neous.   Explain. 

(29.)  The  "luminous 

globe  "  is  represented 

in  Fig.  176.  and  the 

"luminous  tube  "  in  Fig.  177.  The  first  of  these 
consists  of  a  hollow  glass  globe,  on  the  inner 
surface  of  which  small  discs  of  tinfoil  are  placed 
very  near  each  other.  The  first  disc  is  in  con- 
nection with  the  prime  conductor,  and  the  last 
one,  with  the  ground.  When  the  machine  is 
worked,  bright  sparks  appear  at  each  break 
between  the  discs.  The  construction  and  action 
of  the  luminous  tube  are  similar.  Like  the 
"luminous  pane,"  these  pieces  of  apparatus  are 
intended  for  use  in  the  dark.  All  of  these  lu-  pIG 


FIG.  176. 


234 


ELECTRIC  EXPERIMENTS. 


minous  effects  are  best  exhibited  in  the 
dark. 

(30)  If  two  barometer  tubes,  united 
at  the  top,  be  filled  with  mercury  and 
inverted  over  two  cups  of  mercury,  as 
shown  in  Fig.  178,  a  Torricellian  vacuum 
will  be  formed.  When  the  mercury  of 
one  cup  is  connected  with  the  prime  con- 
ductor and  the  other  with  the  earth,  the 
upper  part  of  the  tube  (containing  only 
mercuric  and  other  vapors)  is  filled  with 
light.  The  luminosity  may  be  increased 
by  raising  the  temperature  and  thus  in- 
creasing the  density  of  the  aeriform  con- 
ductor. (A  true  vacuum  will  not  conduct 
electricity. ) 

(31.)  "Geissler's  Tubes"  for  electric 
light  are  sealed  glass  tubes  containing 
a  highly  rarefied  vapor  or  gas,  with  which 
the  tubes  were  filled  before  the  exhaus- 
tion. Platinum  wires  are  sealed  into  the 
glass  at  each  end,  to  conduct  the  elec- 
tric current.  The  brilliancy  and  beauty 
of  the  light,  the  great  variety  of  effects, 
^^^  color,  and  fluorescence,  are  indescribable. 

They  are  made  in  great  variety  of  form  and  size  and  filled  with 


FIG.  178. 


FIG.  179. 

rarefied  vapors  and  gases  of  many  kinds.     A  few  of  the 
forms  are  represented  in  Fig.  179. 

(32.)  On  the  glass  table  of  the  universal  discharger  (Fig.  171) 
place  a  piece  of  wood  and  bring  the  knobs  of  the  sliding  rods  against 
its  ends  so  that  the  line  joining  the  knobs  shall  be  in  the  direction 
of  the  fibers  of  the  wood.  Through  the  apparatus  thus  arranged, 
discharge  a  powerful  battery.  The  piece  of  wood  will  be  torn  in 
pieces. 

(33.)  Support  a  pane  of  glass  upon  a  glass  cylinder,  in  the  axis 
of  which  is  a  pointed  conductor  which  just  touches  the  pane.  On 


ELECTRIC  EXPERIMENTS. 


235 


the  upper  side  of  the  pane  directly  over  this  pointed  conductor  place 
a  drop  of  oil.     From  an  insulated  support  lower  a  second  pointed 


FIG.  1 80. 

conductor  until  it  touches  the  pane  at  the  oil.  Through  these  two 
pointed  conductors  (Fig.  180)  discharge  a  Leyden  jar  or  battery. 
Unless  the  glass  is  very  thin,  a  single  jar  will  not  be  sufficient.  If 
the  experiment  fails  the  first  time,  do  not  use  the  same  piece  of  glass 
for  the  second  trial. 

(34.)  With  corks,  plug  the  ends  of  a  glass  tube  filled  with  water. 
Through  the  corks,  introduce  copper  wires  until  the  ends  in  the 
water  are  within  a  quarter  of  an  inch  of  each  other.  Through 
these  wires  discharge  a  Leyden  jar.  The  mechanical  shock  due  to 
the  repulsion  of  the  electrified  water  molecules  will  break  the  tube. 

(35.)  Fig.  181  represents  "Volta's  Pistol,"  which  consists  of  a 
metal  vessel  through  one  side  of  which  passes  an  insulated  metal 
rod  with  knobs  at  both  ends.  The  knob  at  the 
inner  end  of  this  rod  is  near  the  opposite  wall, 
so  that  a  spark  may  easily  be  made  to  pass 
between  the  knob  and  the  body  of  the  pistol. 
The  pistol  being  filled  with  a  mixture  of  illu- 
minating gas  and  common  air  in  equal  volumes 
or  with  oxygen  and  hydrogen  in  the  proportion 
of  one  volume  of  the  former  to  two  of  the  latter, 
and  the  mouth  being  closed  by  a  cork,  the  pas- 
sage of  the  spark  brings  about  a  chemical  union 
of  the  mixed  gases,  a  violent  explosion  ensues, 
and  the  cork  is  thrown  some  distance.  The  FTG.  181. 


236  ELECTRICITY  AND  EXERGY. 

spark  may  be  produced  by  holding  the  pistol  in  the  hand  and 
bringing  the  outer  knob  near  the  prime  conductor ;  or  the  pistol 
may  be  suspended  from  the  prime  conductor  by  a  wire  or  chain  and 
the  pistol  then  touched  with  the  hand.  The  pistol  may  be  fired  by 
means  of  the  electrophorus  (§  343)  or  Cottrell's  Rubber. 

372.  Relation  of  Electricity  to  Energy.— The 
work  necessarily  performed  in  operating  an  electric  machine 
is  not  all  expended  in  overcoming  inertia  and  friction. 
Much  of  it  is  employed  in  producing  electric  separation. 
It  matters  not  whether  this  separation  be  the  separation  of 
two  fluids  or  of  something  else.  Whatever  be  the  nature 
of  the  realities  separated,  mechanical  kinetic  energy  is 
employed  in  the  separation  and  converted  into  the  poten- 
tial variety  (§  159).  In  every  case  of  electric  attraction  or 
repulsion  we  have  an  evident  reconversion  of  this  potential 
into  mechanical  kinetic  energy.  We  shall  soon  see  that 
the  sound,  heat  and  light  accompanying  electric  discharges 
are  forms  of  energy  due  to  the  conversion  of  the  potential 
energy  of  electric  separation. 

EXERCISES. 

1.  (a.)  If  a  gold-leaf  electroscope  be  placed  within  a  tin  pail  which 
is  insulated  and  electrified,  what  will  be  the  action  of  the  electro 
scope?    (6.)  Explain. 

2.  (a.)  Why  may  one  obtain  a  stronger  spark  from  a  Leyden  jar 
than  from  the  machine  by  which  it  is  charged  ?    (&.)  A  Leyden  jar 
standing  upon  a  glass  plate  cannot  be  strongly  charged.     Why  ? 

3.  (a.)  A  globe  that  is  polished  will  remain  electrified  longer  than 
one  that  is  not  polished.     Why  ?    (&.)  Can  you  devise  an  appendage 
to  the  outer  coat  of  a  Leyden  jar,  so  that  it  may  be  charged  when 
standing  upon  a  plate  of  glass  ? 

4.  (a.)  Can  you  see  any  connection  between  electric  induction  and 
the  fact  that  electricity  dwells  only  upon  the  outer  surface  of  a  con- 
ductor?   (6.)  Describe  the  plate  electric  machine,     (c.)  Explain  its 
action,    (d.)  Explain  the  action  of  the  electrophorus. 


VOLTAIC  ELECTRICITY.  237 

5.  (a.)  A  minute  after  the  discharge  of  a  Leyden  jar,  a  second  and 
feebler  spark  may  generally  be  obtained.    Explain  (§  356.)   (&.)  State 
two  uses  of  lightning-rods. 

6.  (a.}  Having  a  metal  globe  positively  electrified,  how  could  you 
with  it  negatively  electrify  a  dozen  globes  of  equal  size  without 
affecting  the  charge  of  the  first  ?    (6.)  How  could  you  charge  posi- 
tively one  of  the  dozen  without  affecting  the  charge  of  the  first  ? 

7.  Can  you  devise  a  plan  by  which  a  series  of  Leyden  jars,  placed 
upon  a  glass  plate,  may  be  simultaneously  charged,  the  first  posi- 
tively, the  second  negatively,  the  third  positively,  the  next  nega- 
tively, and  so  on  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Condensation  of  electricity ;  the  Leyden  Jar  ; 
the  Leyden  Battery ;  the  Distribution  of  elec- 
tricity on  conductors;  Atmospheric  Electricity; 
electrified  Clouds  and  Lightning ;  Lightning 
Rods  and  their  action  ;  the  Velocity  of  the  electric 
current  and  the  Duration  of  the  electric  spark;  six 
Classes  of  Effects  of  electricity  and  many  electric 
experiments. 


IV. 


VOLTAIC    ELECTRICITY.—  DYNAMO-ELECTRICITY 
AND    THERMO-ELECTRICITY. 

373.  Chemical  Action.—  All  chemical  changes 
produce  electric  separation.  This  is  true  whether  the 
substances  subjected  to  chemical  action  be  solid,  liquid  or 
aeriform  ;  but  the  chemical  action  between  liquids  and 
metals  gives  results  the  most  satisfactory.  Electricity 
thus  developed  is  called  Voltaic  or  Galvanic  electricity. 


VOLTAIC  ELECTRICITY. 


374.  The  Electric  Current. — When  a  strip  of 
copper  and  one  of  zinc  are  placed  in 

dilute  sulphuric  acid,  the  two  strips 
being  connected  above  the  acid  by  a 
wire  conductor,  a  current  of  elec- 
tricity is  produced.  In  fact,  two 
currents,  opposite  in  kind  and  direc^ 
tion,  are  simultaneously  produced, 
but  to  avoid  confusion  the  negative 
current  is  ignored.  When  refer- 
ence is  made  to  the  direction 
of  the  current,  it  means  the  direction  of  the  positive 
current.  The  apparatus  here  described  is  called  a  Voltaic 
or  Galvanic  element. 

375.  Direction  of  the  Current.— For  this  pro- 
duction of  the  electric  current,  it  is  necessary  that  the 
liquid  have  a  greater  action  upon  one  metal  than  upon 
the  other.     The  metal  most  vigorously  acted  upon  con- 
stitutes the  generating  or  positive  plate ;   the  other,  the 
collecting  or  negative  plate.     This  relation  of  the  plates 
determines  the  direction  of  the  current.     In  the  liquid, 
the   current  is  from   the  positive  to  the  negative 
plate;    in  the  mire,  it  is  from  the  negative  to  the 
positive. 

376.  The   Electric    Circuit.— When    the  wires 
from  the  two  plates  are  in  contact,  it  is  said  that  the 
circuit  is  closed;  when  the  plates  are  not  thus  in  electric 
connection  it  is  said  that  the  circuit  is  broken. 

(a.)  When  the  circuit  is  closed,  hydrogen  is  set  free  by  the  decom- 
position of  the  liquid  and  rises  from  the  surface  of  the  negative 
plate.  The  tendency  of  the  hydrogen  to  adhere  to  the  plate  is  one 


VOLTAIC  ELECTRICITY.  239 

of  the  practical  difficulties  to  be  overcome  in  working  a  Voltaic 
element  or  battery. 

377.  Electrodes.— It  will  be  readily  understood  by 
keeping  in  mind  the  direction,  of  the  two  currents,  that, 
if  the  circuit  be  broken,  negative  electricity  will  accumu- 
late at  the  end  of  the  wire  attached  to  the  positive  plate, 
and  positive  electricity  at  the  end  of  the  wire  attached  to 
the  negative  plate.     These  ends  of  the  wires  are  then 
called   poles   or   electrodes.      The    negative   pole   is 
attached  to  the  positive  plate  and  vice  versa.    For 
many  experimental  purposes,  strips  of  platinum  are  fastened 
to  the  ends  of  the  wires ;  these  platinum  strips  then  con- 
stitute the  electrodes. 

378.  Resistance. — Even  a  good  conductor  (§  333)  offers  a 
sensible  resistance  to  the  passage  of  an  electric  current ;  the  poorer 
the  conductor,  the  more  resistance  it  offers  to  the  passage  of  the 
current.     Experiments  show  that  the  quantity  of  electricity  passing 
in  a  unit  of  time,  over  a  given  conductor,  is  directly  proportional  to 
the  electromotive  force.    (This  electromotive  force,  "  K  M.  F."  is 
the  supposed  force  that  causes  or  tends  to  cause  a  transfer  of  elec- 
tricity from  one  point  to  another.)    When  the  E.  M.  F.,  the  sec- 
tional area  and  the  material  are  constant,  the  resistance  is  propor- 
tional to  the  length  of  the  conducting  wire  ;  doubling  the  length 
doubles  the  resistance  and  halves  the  current.    When  the  E.  M.  F., 
the  length  and  material  are  constant,  the  resistance  is  inversely 
proportional  to  the  area  of  the  cross-section  of  the  wire  ;   halving 
that  area  doubles  the  resistance  and  halves  the  current.     Hince  the 
resistance  is  inversely  proportional  to  the  area  of  the  cross-section, 
it  will  also  be  proportional  to  the  weight  of  the  wire  per  unit  of 
length.     The  difference  between  the  resistance  of  a  good  conductor 
and  that  of  an  insulator  is  very  great.     The  resistance  of  a  silver 
wire  being  taken  as  unity,  the  resistance  of  a  similar  wire  of  Ger- 
man silver  would  be  12.82,  while  that  of  a  similar  rod  of  gutta- 
percha  would  be  8.5  x  10-°.    Hence,  insulators  are  often  spoken  of 
as  bodies  of  great  resistance. 

379.  A  Voltaic  Battery. — A  number  of  Vbltaic 
elements   connected   in  such  a   manner  that   the 


240  VOLTAIC  ELECTRICITY. 

current  has  the  same  direction  in  all,  constitutes  a 
Voltaic  battery.  The  usual  method  is  to  connect  the 
positive  plate  of  one  element  with  the  negative  plate  of  the 
next,  as  shown  in  Fig.  183.  When  thus  connected,  they 
are  said  to  be  coupled  "in  series."  Sometimes  all  of  the 
positive  plates  are  connected  by  a  wire,  and  all  of  the  neg- 
ative plates  by  another  wire.  The  cells  are  then  said  to  be 
joined  "in  multiple  arc."  (See  Fig.  184.) 

38O.  Batteries  of  High  and  of  Low  Re- 
sistance.— Each  kind  of  Galvanic  cell  has  an  internal 


FIG.  183. 

resistance,  depending  upon  the  liquid  used,  the  distance 
between  the  plates,  and  the  size  of  the  plates.  The  resist- 
ance of  the  liquid  conductor  is  several  million  times  as 
great  as  that  of  a  similar  metal  conductor.  The  distance 
between  the  plates  determines  the  length  of  the  liquid 
conductor  (§  378),  and  the  size  of  the  plates,  its  area  of 
cross-section.  A  battery  of  cells  joined  in  series  is  called 
a  "battery  of  high  resistance."  A  battery  of  cells  joined 
in  multiple  arc  is  called  a  "  battery  of  low  resistance."  For 
a  long  circuit  of  great  external  resistance,  a  battery  of  high 
resistance  is  needed.  For  a  short  circuit  of  small  external 


VOLTAIC   ELECTRICITY. 


241 


resistance,  large  cells,  or  several  cells  in  multiple  arc  are 
preferable. 

(a.)  A  battery  of  liigli  resistance  was  formerly  called  an  intensity 
battery,  while  a  battery  of  low  resistance  was  called  a  quantity 
battery. 


FIG.  184. 

381,  Daniell's  Battery.— In  the  cell  of  Daniell's 
battery  (Fig.  185),  the  zinc  plate  is  in  the  form  of  a  cleft, 
hollow  cylinder.  Within  this  cylinder  is  a  porous  cup; 
within  the  porous  cup  is  the  copper  cylindrical  plate.  The 
liquid  used  is  dilute  sulphuric  acid,  but  the  acid  within 
the  porous  cup  has  as  much 
copper  sulphate  as  it  can  dis- 
solve, i.  e.y  it  is  saturated.  For 
the  purpose  of  keeping  this 
acid  saturated,  crystals  of  cop- 
per sulphate  are  suspended  in 
it  near  the  surface,  by  means 
of  a  copper  wire  basket  or  per- 
forated earthenware  cup.  The 
effect  of  this  is  to  cause  the 
hydrogen  to  re-enter  into 
chemical  combination  before  it 
reaches  the  copper  plate.  Copper,  instead  of  hydrogen,  is 


FIG.  185. 


242 


VOLTAIC  ELECTRICITY. 


deposited  upon  the  copper  plate.     The  current  from  this 
battery  is  especially  constant. 

(a.)  In  the  figure,  the  copper  plate  is  represented  as  a  cleft 
cylinder  within  the  porous  cup,  the  crystals  being  piled  up  around 
it.  It  is  common  to  interchange  the  plates,  the  zinc  being  in  dilute 
sulphuric  acid  within  the  porous  cup,  and  the  copper  plate  in  the 
saturated  acid  outside  the  porous  cup.  Sometimes  the  outer  vessel 
itself  is  made  of  copper  instead  of  glass,  the  vessel  then  becoming 
the  negative  plate.  The  internal  resistance  of  a  Daniell's  cell  is  as 
great  as  that  of  a  quarter  of  a  mile  of  ordinary  telegraph  wire. 

3S2.  Smee's  Battery. — An  element  of  Smee's 
battery  is  represented  by  Fig.  186.  It 
consists  of  a  silver  plate  coated  with 
platinum  powder  placed  between  two  zinc 
plates,  the  plates  being  hung  in  dilate 
sulphuric  acid.  The  use  of  the  pbtiimm 
powder  is  to  free  the  plate  from  the 
liberated  hydrogen. 


FIG.  186. 


383.  Potassium  Bi-chromate 
Battery. — The  potassium  bi-chromate 
battery  differs  from  Smee's  in  the  sub- 
stitution of  a  carbon  plate  for  the  silver 
plate,  and  of  a  solution  of  potassium 
bi-chromate  in  dilute  sulphuric  acid 
for  the  liquid  there  used.  Here  the 
hydrogen  is  given  an  opportunity  for 
chemical  union  as  fast  as  it  is  liberated. 


(<z.)  The  bottle  form  of  this  battery,  repre- 
sented in  Fig.  187,  is  the  most  convenient  for 
the  laboratory  or  lecture  table.  By  means  of 
the  sliding  rod,  the  zinc  plate  can  be  raised 
out  of  the  solution  when  not  in  use  ;  and  thus 
adjusted,  the  cell  can  remain  for  months  with- 
out any  action,  if  desired,  and  be  ready  at  a 
moment's  notice.  One  of  the  best  proper  - 


FIG.  187. 


VOLTAIC  ELECTRICITY. 


243 


FIG.  188. 


tions  for  the  solution  is  as  follows  :  One  gallon  of  water,  one  pound 
of  bi  cliromate  of  potash,  and  from  a  half -pint  to  a  pint  of  sulphuric 
acid,  according  to  the  energy  of  action  desired.  A  small  quantity 
of  nitric  acid  added  to  the  solution  increases  the  constancy  of  the 
battery. 

{&.)  The  following  recipe  is  good  :  Pour  187  CM.  cm.  of  sulphuric 
acid  into  500  cu.  cm.  of  water,  and  let  the  mixture  cool.  Dissolve 
115  g.  of  potassium  bi-chromate  in  335  cu.  cm.  of  boiling  water,  and 
pour  while  hot  into  the  dilute  acid.  When  cool  it  is  ready  for  use. 

384.  Grove's    Battery.  — The 

outer  vessel  of  an  element  of  Grove's 

battery  contains  dilute  sulphuric  acid. 

In  this  is  placed  a  hollow  cylinder  of 

zinc.     Within  the  zinc  cylinder  is  placed 

a  porous  cup  containing  strong  nitric 

acid.    The  negative  plate  is  a  strip  of 

platinum  placed  in  the  nitric  acid.    The 

hydrogen  passes  through  the  porous  cup  and  reduces  the 

nitric  acid  to  nitrogen  peroxide,  which  escapes  as  brownish 

red  fumes.    A  Grove's  element  is  represented  in  Fig.  188. 

385.  Bimsen's  Battery. — Bunsen's  battery  differs 

from  Grove's  in  the  use  of  car- 
bon instead  of  platinum  for 
the  negative  plate.  The  ele- 
ments are  made  larger  than 
for  Grove's  battery.  It  gives 
greater  quantity  and  less  in- 
tensity than  Grove's  (§  380  [a]). 
A  Bunsen's  element  is  repre- 
sented in  Fig.  189. 

p        g  Note. — There  are  scores  of  dif- 

ferent batteries  in  the  market  com- 
peting for  favor.  With  the  exception  of  Smee's,  those  here 
described  are  the  ones  most  commonly  used. 


244  VOLTAIC  ELECTRICITY. 

386.  Amalgamating  the  Zinc.— Ordinary  com- 
mercial zinc  is  far  from  being  pure.     Chemically  pure  zinc 
is  expensive.    When  impure  zinc  is  used,  small  closed  cir- 
cuits are  formed  between  the  particles  of  foreign  matter 
and  the  particles  of  zinc.     This  local  action  rapidly  destroys 
the  zinc  plate  and  contributes  nothing  to  the  general  cur- 
rent.   This  waste,  which  would  not  occur  if  perfectly  pure 
zinc  were  used,  is  prevented  by  frequently  amalgamating 
the  zinc.      This  is  done  by  cleaning  the  plate  in  dilute 
acid  and  then  rubbing  it  with  mercury. 

(a.)  The  method  of  amalgamating  battery  zincs  practised  by  the 
author  is  as  follows  :  In  a  glass  vessel  placed  in  hot  water,  dissolve 
15  cu.  cm.  of  mercury  in  a  mixture  of  170  cu.  cm.  of  strong  nitric 
acid  and  625  cu.  cm.  of  chlorhydric  (muriatic)  acid.  When  the 
mercury  is  dissolved,  add  830  cu.  cm.  of  chlorhydric  acid.  When 
the  liquid  has  cooled,  immerse  the  battery  zinc  in  it  for  a  few 
minutes,  remove  and  rinse  thoroughly  with  water.  The  liquid  may 
be  used  over  and  over  until  the  mercury  is  exhausted.  The  quan- 
tity here  mentioned  will  suffice  for  200  ordinary  zincs  or  more. 
Keep  the  liquid,  when  not  in  use,  in  a  glass-stoppered  bottle. 

387.  Thermal  Effects  of  Voltaic  Electric- 
ity.— When  a  strong  current  is  passed  over  a  very  thin 
wire  made  of  a  poor  conductor,  as  platinum  or  even  iron, 
the  resistance  develops  heat  which  may  render  the 
wire  incandescent  or  even  fuse  or  vaporize  it.    Thus 
the  Voltaic  current  is  often  used  in  firing  mines  in  mili- 
tary operations  and  blasting.     (See  §  389.) 

(a.)  If  stout  copper  wires  from  the  two  plates  of  a  potassium 
bi-chromate  battery  (Fig.  187)  have  their  free  ends  united  by  a  very 
fine  iron  wire,  the  passage  of  the  current  will  heat  it  sufficiently  to 
ignite  gun  cotton.  All  known  metals,  even  iridium  and  platinum, 
have  been  melted  in  similar  manner,  while  carbon  rods  have  been 
heated  by  a  battery  of  600  Bunsen's  elements  until  they  softened 
enough  for  welding. 


VOLTAIC  ELECTRICITY. 


245 


388.  Luminous  Effects.— When  the  circuit  of  a 
battery  is  closed  or  broken  there  is  a  spark  at  the  point  of 
contact.  Beautiful  luminous  effects  may  be  produced  by 
winding  the  wire  from  one  plate  about  the  end  of  a  file, 
and  drawing  the  other  electrode  along  the  side  of  the  fiie, 
thus  rapidly  closing  and  breaking  the  circuit. 


389.  The  Voltaic 
Arc. — The  most  bril- 
liant luminous  effect  of 
current  electricity  is  the 
Voltaic  arc  or  electric 
lamp.  The  electric  lamp 
consists  essentially  of 
two  pointed  bars  of  gas 
carbon  placed  end  to 
end  in  the  circuit  of  a 
very  powerful  current. 
If  the  ends  of  the  car- 
bons be  separated  a 
short  distance  while  the 
current  is  passing,  the 
carbon  points  become 
incandescent  and  the 
current  "will  not  be  in- 
terrupted. W^^en  the 
carbons  are  thus  sep- 
arated, the  space  'be- 
tween is  filled  with 
a  luminous  arc,  the 
'brilliancy  of  which 
exceeds  that  of  any 


THE  BRUSH  ELECTRIC  LAMP. 


FIG.  190. 


246 


VOLTAIC  ELECTRICITY. 


other  light  under  human  control,  the  temperature 
of  which  is  unequalled  &T/  any  other  artificial  source 
of  heat. 

39O.  Deflection  of  the  Magnetic  Needle.— 

The  Voltaic  current  has  a  marked  effect  in  the  deflection 
|  of  the  magnetic  needle,  and  tends  to 
place  the  needle  at  right  angles  to 
the  direction  of  the  current.  This 
may  be  easily  shown  by  Oersted's 
apparatus  represented  in  Fig.  191. 
It  consists  of  a  magnetic  needle  and 
a  brass  wire  frame  with  three  pole- 
FIG.  191.  cups,  permitting  the  current  to  be 

passed  over,  under,  or  around  the  magnet. 

(a.)  If  tlie  current  pass  above  the  needle  from  north  to  south,  the 
—  end  of  the  magnet  (§  317)  will  be  deflected  toward  the  east ; 
if  it  pass  from  south  to  north,  the  —  end  of  the  needle  will  be 
deflected  toward  the  west.  If  the  current  pass  below  the  needle, 
the  deflections  will  be  the  opposite  of  those  just  mentioned. 

S91.  The  Galvanometer. — The  galvanometer  de- 
pends upon  the  principles  set  forth  in 
the  last  article.  It  is  a  very  delicate 
piece  of  apparatus  for  detecting 
the  presence  of  an  electric  current 
and  determining  its  direction  and 
intensity.  In  Oersted's  apparatus  the 
needle  is  heavy,  and  a  considerable 
force  is  needed  to  set  it  in  motion ; 
in  the  galvanometer  the  needle  is  very 
light,  and  is  easily  set  in  motion. 
In  Oersted's  apparatus  the  needle  is 
held  in  the  magnetic  meridian  by  the  directive  influence 


VOLTAIC  ELECTRICITY.  247 

of  the  earth  ;  in  the  galvanometer  this  is  obviated  almost 
wholly  by  the  use  of  an  astatic  needle.  In  Oersted's 
apparatus,  the  current  makes  but  a  single  course  about 
the  needle;  in  the  galvanometer,  the  covered  wire  is 
coiled  many  times  about  the  needle  and  thus  the  effect  is 
multiplied.  Cue  of  the  needles  is  within  the  coil  while  the 
other  swings  above  it,  the  two  being  connected  by  a 
vertical  axis  passing  through  an  appropriate  slit  in  the  coil. 
If  both  needles  were  within  the  coil,  since  their  poles  are 
reversed  (§  314),  the  same  current  would  tend  to  deflect 
them  in  opposite  directions  and  thus  the  action  of  one  needle 
would  neutralize  that  of  the  other.  The  astatic  needle  is 
suspended  by  an  untwisted  silk  fibre  from  a  hook  which 
may  be  lowered  when  the  instrument  is  not  in  use  until  the 
upper  needle  rests  upon  the  dial  plate  beneath  it.  The  ends 
of  the  coiled  wire  are  connected  with  bin  ding  screws;  level- 
ling screws  are  provided,  by  means  of  which  the  instrument 
may  be  adjusted  so  that  the  needles  shall  swing  clear  of  all 
obstructions.  A  glass  cover  protects  from  dust  and  dis- 
turbance by  air  currents.  The  instrument  is  represented 
in  Fig.  192. 

392.  Magnetic  Effects  of  the  Voltaic  Cur- 
rent.— A  bar  of  soft  iron  may  be  easily 
magnetized  by  the  inductive  influence  of 
the  Voltaic  current.     This  is  shown  by 
the  action  of  the  bar  and  helix  (Fig.  193). 

(a.)  Tliis  apparatus  consists  of  a  movable  bar  FIG. 

of  soft  iron  surrounded  by  a  coil  of  insulated 
copper  wire.     When  the  wire  of  the  coil  is  placed  in  the  closed 
circuit  of  a  battery,  the  iron  bar  becomes  strongly  magnetized  ; 
when  the  circuit  is  broken,  the  bar  instantly  loses  its  magnetic 
power.     The  same  thing  is  illustrated  by  the  ' '  helix  and  ring 


248 


VOLTAIC  ELECTRICITY 


armature"  shown  in  Fig.  194.  The  armature  is  of  soft  iron 
divided  into  two  semicircles  with  brass  handles. 
When  the  helix  is  placed  in  a  closed  circuit,  the 
semicircles  resist  a  considerable  force  tending  to 
draw  them  apart;  when  the  circuit  is  broken  they 
fall  asunder  of  their  own  weight. 


393.   Electro-Magnets.— The  bar  of 

Fig.  193,  and  the  ring  of  Fig.  194,  are  electro- 
magnets. The  electro-magnet  more  often  has 
the  horse-shoe  form  shown  in  Fig.  195.  The 

middle  of  the  bent  bar  is  bare,  the  direction  of  the  windings 

on  the  ends  being  such  that,  were  the  bar  straightened,  the 

current  would  move  in  the  same 

direction     round     every    part. 

Electro-magnets  have  been  made 

capable    of    supporting    several 

tons. 

(a.)  When  the  circuit  is  broken  and 
the  current  thus  interrupted,  the  iron 
is  generally  not  wholly  demagnetized. 
The  small  magnetism  remaining  is 
called  residual  magnetism.  The  resid- 
ual magnetism  seems  to  vary  with 
the  degree  of  impurity  of  the  iron. 

394.  Making  Perma- 
nent Magnets.— A  steel  bar 
may  be  permanently  magnetized 
(§  320)  by  drawing  it,  from  its  centre,  in  one  direction  over 
one  pole  of  a  powerful  electro-magnet,  and  then,  from  its 
centre,  in  the  opposite  direction  over  the  other  pole,  and 
repeating  the  process  a  few  times.  A  bar  of  steel  placed 
within  a  helix  through  which  a  strong  current  is  passing, 
will  be  permanently  magnetized.  The  arrangement  is  sub- 
stantially like  that  shown  in  Fig.  193. 


FIG.  195. 


VOLTAIC  ELECTRICITY. 


249 


395.  The  Electric  Telegraph.—  The  electric  tele- 
graph consists  essentially  of  an  electro-magnet  and  a  "  key  " 
placed  in  the  circuit  of  a  battery.     The  key  is  an  instru- 
ment by  which  the  circuit  may  be  easily  broken  or  closed 
at  will.    The  armature  of  the  magnet  is  supported  by  a 
spring,  which  lifts  it  when  the  circuit  is  broken.    When 
the  circuit  is  closed,  the  armature  is  drawn  down.    Thus 
the  armature  may  be  made  to  vibrate  up  and  down  at  the 
will  of  the  person  at  the  key.    The  armature  may  act  upon 
one  arm  of  a  lever,  the  other  end  of  which,  being  provided 
with  a  style  or  pencil,  may  be  pressed  a.gainst  a  strip  ot 
paper  drawn  along  by  clock-work.    Thus  the  pencil  may 
be  made  to  record,  upon  the  moving  paper,  a  series  of  dots 
and  lines  at  the  pleasure  of  the  operator  at  the  key  perhaps 
hundreds  of  miles  away.     When   the  two  stations  are 
several  miles  apart,  one  of  the  wires  is  dispensed  with,  the 
circuit  being  completed  by  the  earth. 

396.  Morse's    Alphabet.—  The  inventor  of  the 
electric  telegraph  was  an  American,  S.  F.  B.  Morse.    The 
system  of  signals  devised  by  him  is  given  below  : 


LETTERS. 


j  

s 

k  

t 

1  

u 

m  

V 

n  

w 

o  -    - 

X 

7/ 

q  

y 

z 

r  . 

& 

FIGURES. 

1  ---- 

2  ----- 

3  ----- 

4  ----- 

5  --- 
C  ...... 

7  ---- 

8  ----- 

9  ---- 
0  _ 


To  prevent  confusion,  a  small  space  is  left  between  successive 
letters,  a  longer  one  between  words,  and  a  still  longer  one  between 
sentences.  Telegraph  operators  soon  become  so  familiar  with  this 


250 


VOLTAIC  ELECTRICITY. 


alphabet  that  they  understand  a  message  from  the  mere  clicks  of 
the  lever,  and  do  not  use  any  recording  apparatus. 

397.  Chemical  Effects  of  the  Voltaic  Cur- 
rent.— Many  chemical  compounds  in  solution  may  be 


FIG.  196. 

decomposed  by  forcing  the  current  to  traverse  the  solution. 
Substances  which  are  thus  decomposed  are  called  electro- 
lytes ;  the  process  is  called  electrolysis;  the  compound  is 
said  to  be  elect roly zed.  The  electrolysis  of  water  is  easily 
accomplished,  affording  a  satisfactory  qualitative  and  quan- 
titative analysis  of  the  liquid. 

(a.)  The  apparatus  consists  of  a  vessel  (Fig.  196)  containing  water 
(to  which  a  little  acid  has  been  added  to  increase  its  conductivity) 
in  which  are  immersed  two  platinum  strips  which  constitute  the 
two  electrodes  of  a  battery.  When  the  circuit  is  closed,  bubbles  of 
oxygen  escape  from  the  positive  electrode  and  bubbles  of  hydrogen 
from  the  negative.  The  gases  may  be  collected  separately  by 
inverting  over  the  electrodes  tubes  filled  with  water  as  shown  in 
the  figure.  The  volume  of  hydrogen  thus  collected  will  be  twice 
as  great  as  that  of  the  oxygen. 

398.  Electrolysis  of  Salts.— Into  a  bent  tube  (known  to 


VOLTAIC  ELECTRICITY. 


251 


dealers  in  chemical  glassware  as  a  U  tube)  put  a  solution  of  any 
neutral  salt,  e.  g.,  sodium  sulphate.  Color  the 
contents  of  the  tube  with  the  solution  from  purple 
cabbage.  In  the  arms  of  the  tube  place  the  plati- 
num electrodes  of  a  battery  as  shown  in  Fig.  197. 
Close  the  circuit  and  presently  the  liquid  at  the 
+  electrode  will  be  colored  red  and  that  at  the  — 
electrode,  green.  If,  instead  of  coloring  the  solu- 
tion, a  strip  of  blue  litmus  paper  be  hung  near 
the  +  electrode  it  will  be  reddened,  while  a  strip 
of  reddened  litmus  paper  hung  near  the  —  elec- 
trode will  be  colored  blue.  Ttiese  changes  of  color 
are  chemical  tests;  the  appearance  of  the  green  or 
blue  denotes  the  presence  of  an  alkali  (caustic  soda  in  this  case), 
while  the  appearance  of  the  red  denotes  the  presence  of  an  acid. 

399.  Electro-plating  and  Electro -gilding.— 

From  the  -f-  pole  of  a  galvanic  battery  suspend  a  plate  of 
copper;  from  the  —  pole,  suspend  a  silver  coin.  Place 
the  copper  and  silver  electrodes  in  a  strong  solution  of 
copper  sulphate.  When  the  circuit  is  closed,  the  salt  of 
copper  is  electrolyzed,  the  copper  from  the  salt  being 


FIG.  197. 


FIG.  198. 

deposited  upon  the  silver  coin,  the  sulphuric  acid  going  to 
the  copper  or  +  electrode  as  it  did  in  the  experiment 
described  in  the  last  paragraph.    The  silver  is  thus  copper- 
plated. 
(a.)  If  a  solution  of  some  silver  salt  be  used  and  the  direction  of 


252  VOLTAIC  ELECTRICITY. 

the  current  be  reversed,  silver  will  be  deposited  upon  the  copper 
plate,  which  will  thus  be  silver-plated.  If  the  positive  electrode  be 
a  plate  of  gold  and  the  bath  a  solution  of  some  salt  of  gold  (cyanide 
of  gold  dissolved  in  a  solution  of  cyanide  of  potassium),  gold  will 
be  deposited  upon  the  copper  of  the  negative  electrode,  which  will 
be  thus  electro-gilded. 

4OO.  Electrotyping.  —  Impressions  are  taken  from 
type  or  engravings  in  wax,  or  any  other  plastic  material 
that  is  impervious  to  water.  A  conducting  surface  is  given 
to  such  a  mould  by  brushing  finely-powdered  graphite  over 
it,  and  it  is  then  placed  in  a  solution  of  sulphate  of  copper 
facing  a  copper  plate.  The  mould  is  then  connected  with 
the  -f  plate  of  a  Galvanic  battery  and  the  copper  with 
the  —  plate  ;  when  the  circuit  is  closed,  copper  will  be 
deposited  upon  the  mould.  "When  the  copper  film  is  thick 
enough  (say  as  thick  as  an  ordinary  visiting  card)  it  is 
removed  from  the  mould,  and  strengthened  by  filling  up 
its  back  with  melted  type-metal.  The  copper  film  and 
the  type-metal  are  made  to  adhere  by  means  of  an  amalgam 
of  equal  parts  of  tin  and  lead.  The  copper-faced  plate 
thus  produced  is  an  exact  reproduction  of  the  type  and 
engravings  from  which  the  mould  was  made. 


e.  —  It  will  be  noticed  that  in  all  these  cases  the  metal  is 
carried  in  the  direction  of  the  current  and  deposited  upon  the  neg- 
ative electrode.  In  electro-plating  and  gilding,  the  technicalities 
of  the  art  refer  chiefly  to  the  means  of  making  the  deposit  firmly 
adherent.  In  electrotyping,  they  refer  chiefly  to  the  preparation 
of  the  mould  or  matrix.  The  countless  applications  of  this  process 
of  depositing  a  thin  metallic  coat  on  a  body  prepared  for  its  recep- 
tion, constitute  the  important  art  of  electro-metallurgy. 

4O1.  Electro  -chemical  Series.  —  The  facts  just 
considered  suggest  a  division  of  substances  into  two  classes, 
electro-positive  and  electro-negative.  The  constituent 
of  an  electrolyte  that  goes  to  the  negative  electrode 


VOLTAIC  ELECTRICITY.  253 

is  called  electro-positive;  that  which  goes  to  the 
positive  electrode  is  called  electro-negative,  these 
terms  being  based  upon  the  idea  of  attraction  between 
opposite  electricities. 

402.  Physiological  Effects  of  Voltaic  Elec- 
tricity.— The  physiological  effects  are  shocks  and  spas- 
modic muscular  contractions  more  or  less  violent.    When 
the  electrodes  of  a  strong  battery,  or  the  electrodes  of  a 
Ruhmkorff  coil  (§  410),  are  held  in  moistened  hands,  the 
passage  of  the  current  through  the  body  produces  a  pecu- 
liar sensation  easily  recognized  thereafter.     The  current 
may  be  made  to  pass  through  a  series  of  persons  who  have 
joined  hands. 

403.  Induced    Currents.— From    our  study  of 
f rictional  electricity,  we  are  familiar  with  the  term  induc- 
tion, by  which  we  understand  the  influence  which  an 
electrified  body  exerts  upon  a  neighboring  unelectrified 
body.    In  1831,  Faraday  discovered  an  analogous  class  of 
phenomena  produced  by  Voltaic  electricity  or  by  mag- 
netism.   An  induced  cun*ent  is  an   instantaneous 
cuwent  produced  in  a  conductor  by  the  influence 
of  a  neighboring  current  or  magnet.    A  current  used 
to  produce  such  an  effect  is  called  an  inducing  current. 

404.  Inductive  Effect  of  Closing  or  Break- 
ing a  Circuit. — In  Fig.  199,  B  represents  a  double 
coil  made  as  follows:   On  a  hollow  cylinder  of  wood  or 
card-board  is  wound  several  layers  of  stout  copper  wire, 
insulated  by  being  covered  with  silk.     The  two  ends  of 
this  wire,  which  constitute  the  primary  coil,   are  seen 
dipping  into  the  cups  gcj '.    Upon  this  coil,  and  carefully 
insulated  from  it,  is  wound  a  much  greater  length  of  finer 


254 


VOLTAIC  ELECTRICITY. 


copper  wire,  also  silk  covered.  The  two  ends  of  this  wire, 
which  constitute  the  secondary  coil,  are  seen  connecting 
with  the  galvanometer  O.  Wires  from  the  two  plates  of 
a  Voltaic  element  dip  into  mercury  in  the  cups  gg'9  thus 
closing  an  inducing  circuit  through  the  primary  coil. 
While  this  circuit  is  closed,  the  galvanometer  is  at  rest, 
showing  that  no  current  is  passing  through  the  secondary 
coil.  By  lifting  one  of  the  wires  from  one  of  the  cups, 
the  inducing  current  is  interrupted.  At  this  instant  the 
galvanometer  needle  is  deflected  as  by  a  sudden  impulse, 


FIG.  199. 

which  immediately  passes  away.  This  shows  the  existence 
of  an  instantaneous  induced  current  in  the  secondary  coil. 
The  direction  in  which  the  needle  was  turned,  shows  that 
the  secondary  current  was  direct,  i.  e.,that  it  had  the  same 
direction  as  the  inducing  current.  If  the  wire  just  removed 
from  the  cup  be  replaced  and  the  inducing  current  thus 
re-established,  the  galvanometer  needle  will  be  momenta- 
rily turned  in  the  direction  opposite  to  that  in  which  it 
was  previously  turned.  These  experiments  lead  to  this 
conclusion :  ~\^en  a  current  begins  to  flow  through 
the  primary  coil,  it  induces  an  inverse  current  in 
the  secondary  coil;  when  it  ceases  to  flow  through 


VOLTAIC  ELECTRICITY. 


255 


the  primary  coil,  it  induces  a  direct  current  in  the 
secondary  coil;  both  induced  currents  are  merely 
instantaneous. 

4O5.  Currents  Induced  by  Change  of  Dis- 
tance.— If  the  primary  coil  be  made  movable,  as  shown 
in  Fig.  200,  and,  with  a  current  passing  through  it,  be 
suddenly  placed  within  the  secondary  coil,  the  galvanom- 
eter will  show  that  an  inverse  current  was  induced  in  the 
outer  coil.  When  the  needle  has  come  to  rest,  let  the 
primary  coil  be  removed,  and  the  galvanometer  will  show 
that  a  direct  current  was  induced. 
From  this  we  see  that  when  the 
primary  coil,  bearing  a  cur- 
rent, is  brought  near  the  sec- 
ondary coil,  a  momentary 
inverse  current  is  induced  in 
the  latter;  that  ivhen  the 
coils  are  separated,  a  direct 
current  is  induced. 

4O6.  Magneto -electric 
Induction. — If,  instead  of  the 
primary  coil  bearing  the  inducing 

current,  a  bar  magnet  be  used,  as 
FIG.  200.  ghown  in  Fig>  2Q1^  the  results 

produced  will  be  like  those  stated  in  the  last  paragraph. 
Wlien  the  magnet  is  thrust  into  the  interior  of  the 
coil,  an  induced  current  will  flow  while  the  motion 
of  the  magnet  continues.  ]Vhen  the  magnet  is 
stationary  the  current  ceases  to  flow,  and  the  needle 
gradually  comes  to  rest.  When  the  magnet  is  with- 
drawn, an  induced  current  flows  in  the  opposite 
direction. 


256 


VOL  TA  1C  ELECTRICITY. 


FIG.  201. 


4O7.  The  Inductive  Action  of  a  Temporary 
Magnet. — If  within  the  coil  a  soft  iron  bar  (or  still 
better,  a  bundle  of  straight  soft,  iron  wires)  be  placed,  as 


FIG.  202. 


shown  in  Fig.  202,  the  induced   current  may  be  more 
effectively  produced  by  bringing  one  end  of  a  permanent 


VOLTAIC  ELECTRICITY.  257 

magnet  near  the  end  of  the  soft  iron.  In  this  case  the 
induced  currents  are  due  to  the  magnetism  of  the  soft 
iron,  this  magnetism  being  due  to  the  inductive  influence 
of  the  magnet  (§  311).  Thus  we  see  that  when  the  in- 
tensity of  the  magnetism  of  a  bar  of  iron  is  in- 
creased or  diminished,  currents  are  induced  in  the 
coil. 


408.  The   Telephonic  Current.  —  An   electric 
current  may  be  induced  in  a  coil  of  insulated  wire  sur- 
rounding a  bar  magnet  by  the  approach  and  withdrawal 
of  a  disc  of  soft  iron.    The  disc  a  (Fig.  203)  is  magnetized 
by  the  inductive  in- 

fluence of  the  mag- 

net m  (§  311).    The 

disc,    thus    magnet- 

ized.,    reacts    upon 

the  magnet  m  and 

changes   the  distri- 

bution of  magnetism   therein.     By  varying  the  distance 

between  a  and  m,  the  successive  changes  in  the  distribution 

of  the  magnetism  of  m  induce  to-and-fro  currents  in  the 

surrounding  coil. 

409.  The  Telephonic  Circuit.—  If  the  wire  sur- 

rounding the  magnet  mentioned  in  the  last  paragraph  be 
continued  to  a  distance  and  then  wound  around  a  second 
bar  magnet,  as  shown  in  Fig.  204,  the  currents  induced  at 
A  would  affect  the  magnetism  of  the  bar  at  B  (§  392)  or 
the  intensity  of  its  attraction  for  the  neighboring  disc  ~b. 
A  vibratory  motion  in  the  disc  a  would  induce  electric 
currents  at  A  ;  these  currents,  when  transmitted  to  B, 
would  affect  the  magnetism  of  the  bar  there,  and  thus  tend 


258 


VOLTAIC  ELECTRICITY. 


FIG.  204. 

to  produce  exactly  similar  vibrations  in  b.  "It  is  as  if  the 
close  approach  and  quick  oscillation  of  the  piece  of  soft 
iron  fretted  or  tantalized  the  magnet  and  sent  a  series  of 
electrical  shudders  through  the  iron  nerve." 

(a.)  We  have  here  the  principle  of  the  telephone,  so  far  as  elec- 
tric action  is  involved.  Further  consideration  of  this  instrument 
must  be  deferred  until  we  have  learned  more  concerning  sound. 
(See  §  445.) 

41O.  Ruhmkorff's  Coil. — The  induction  coil,  often 
called,  from  the  name  of  its  inventor,  Ruhmkorff's  coil, 
is  a  contrivance  for  producing  induced  currents  in  a 
secondary  coil  by  closing  and  opening,  in  rapid  suc- 
cession, the  circuit  of  a  current  in  the  primary  coil. 

The  axis  of  the 
coils  is  a  bundle 
of  soft  iron  wires. 
These  wires  usu- 
ally terminate  in 
two  small  plates 
of  soft  iron  which 
thus  form  the 

ends  of  the  wire 
FIG.  205 

bundle.   Around 

this  bundle  is  wound  the  primary  coil  of  insulated  copper 


VOLTAIC  ELECTRICITY. 


259 


wire  about  2  mm.  in  diameter.  Upon  the  primary  coil,  but 
carefully  insulated  from  it,  is  wound  the  secondary  coil. 
The  wire  of  the  secondary  coil  is  very  fine  (about  J  mm.) 
and  many  times  longer  than  that  of  the  primary;  two  hun- 
dred and  eighty  miles  of  wire  has  been  put  into  a  secondary 
coil. 

(a.)  The  wire  bundle  becomes  magnetized  (§  392)  by  the  action  of 
current  in  the  primary  coil,  and  then  adds  its  inductive  effect  upon 
the  secondary  coil  to  that  of  the  primary  itself.  The  circuit  is 
broken  and  closed  by  an  automatic  interrupter,  represented  at  the 
left  hand  of  the  coil,  Fig.  205.  One  of  the  posts  there  seen  carries 
a  metallic  vibrating  plate  with  an  iron  disc  at  its  end.  This  plate 
vibrates  back  and  forth  between  the  end  of  the  iron  core  of  the  coils 
and  the  end  of  the  metal  adjusting  screw  which  is  carried  by  the 
other  post  seen  in  the  figure.  These  posts  are  in  the  circuit  of  the 


FIG.  206. 

current  passing  through  the  primary  coil.  When  the  vibrating 
plate  rests  against  the  end  of  the  adjusting  screw,  the  circuit  is 
closed  and  the  iron  core  is  magnetized.  As  soon  as  the  core  is 
magnetized,  it  attracts  the  iron  disc  at  the  end  of  the  vibrating 
plate,  thus  drawing  it  away  from  the  end  of  the  screw  and  break- 
ing the  circuit.  As  soon  as  the  circuit  is  broken,  the  bar  is  de- 
magnetized and  the  plate,  by  virtue  of  its  elasticity,  springs  back  to 


260  VOLTAIC  ELECTRICITY. 

0 

the  screw,  closing  the  circuit  and  again  magnetizing  the  core.  The 
plate  is  thus  made  to  vibrate  with  great  rapidity,  each  oscillation 
making  or  breaking  the  circuit  of  the  inducing  current,  and  thus 
creating  a  series  of  induced  currents  in  the  secondary  coil  (§  404), 
which  produce  effects  greater  than  can  be  produced  by  any  electric 
machine.  Fig.  206  represents  an  induction  coil  made  by  E.  S. 
Ritchie,  of  Boston,  for  the  U.  S.  Military  Academy  at  West  Point. 
In  this  instrument  there  is  no  automatic  interrupter,  the  break-piece 
being  operated  by  a  ratchet-wheel  and  crank. 

411.  Spark  from  Induction  Coil. — If  the  ends 
of  the  secondary  coil  be  connected,  opposite  currents  alter- 
nately traverse  the  connecting  wire.   When  the  ends  are  dis- 
connected, as  shown  in  Fig.  206,  the  inverse  current  cannot 
overcome  the  resistance  of  the  intervening  air  because  of 
its  low  electromotive  power.    The  direct  current,  pro 
duced  by  breaking  the  primary  circuit,  is  alone  able 
to  force  its  way  in  the  form  of  a  spark.    The  sparks 
vary  with  the  power  of  the  instrument.     An  induction  coil 
has  been  made  that  gives  a  spark  over  40  inches  in  length — 
a  result  incomparably  greater  than  that  obtainable  from 
any  electric  machine.     The  induction  coil  may  be  used  to 
produce  any  of  the  effects  of  Motional  electricity,  it  being 
at  the  same  time  nearly  free  from  the  limitations  which 
atmospheric  moisture  places  upon  all  electric  machines. 

Note. — For  an  ordinary  Ruhmkorff' s  coil,  one  to  three  Bunsen  or 
potassium  bi  chromate  elements  will  suffice.  The  effect  of  the  coil 
is  generally  increased  by  placing,  in  the  base  of  the  instrument,  a 
condenser  made  of  many  sheets  of  tinfoil  separated  by  layers  of 
oiled  silk.  Alternate  layers  of  the  tinfoil  are  connected,  t.  e.,  the 
first,  third,  fifth,  seventh,  etc.,  layers  are  connected,  as  also  are  the 
second,  fourth,  sixth,  eighth,  etc.  The  odd  numbered  layers  are 
connected  with  one  end  of  the  primary  coil ;  the  even  numbered 
layers  with  the  other  end.  One  object  of  this  is  to  prevent  the 
spark  otherwise  produced  at  the  break-piece  of  the  primary  circuit. 

412.  Thermo-electricity. — //  a  circuit  be  made 


VOLTAIC  ELECTRICITY, 


261 


FIG.  207. 


of  two  metals  and  one  of  the  junctions  be  heated  or 
chilled,  a  current  of  electricity  is  produced. 

(a.)  This  may  be 
illustrated  by  the 
apparatus  shown 
in  Fig.  207.  The 
upper  bar,  mn, 
having  its  ends 
bent,  is  made  of 
copper  ;  the  low- 
er, op,  is  of  bis- 
muth. This  rect- 
angular frame  is 
to  be  placed  in  the 
magnetic  merid- 
ian and  a  mag- 

netic needle  placed  within  it.  Upon  heating  one  of  the  junctions  a 
current  will  be  produced,  the  existence  of  which  is  satisfactorily 
shown  by  the  deflection  of  the  needle  as  shown  in  the  figure.  The 
junction  may  be  chilled  with  a  piece  of  ice  or  by  placing  upon  it 
some  cotton  wool  moistened  with  ether.  In  this  case  a  current, 
opposite  in  direction  to  the  first,  will  be  produced  ;  the  needle  will 
be  turned  the  other  way  (§  390).  (Appendix,  L.) 

413.  A  Thermo-electric  Pair.  —  If  a  bar  of  anti- 
mony, A,  be  soldered  to  a  bar  of  bismuth,  B,  and  the  free 
ends  joined  by  a  wire,  as  shown  in 
®^>  we  eyidently  have  a  circuit 
B  —      equivalent  to  the  one  considered  in 

the  last  paragraph.  When  the  junc- 
tion C  is  heated  a  current  will  pass  from  bismuth  to  anti- 
mony across  the  junction,  and  from 
antimony  to  bismuth  through  the 
wire. 


(a)  The  arrangement  is  analogous  to 
the  Voltaic  element  (§  374),  the  antimony 
representing  the  —  plate  and  carrying 


B 

FIG.  209. 


262 


VOLTAIC  ELECTRICITY. 


the  +  electrode,  the  bismuth  representing  the  +  plate  and  carrying 
the  —  electrode,  while  the  solder  takes  the  place  of  the  liquid. 
Just  as  a  number  of  Voltaic  elements  may  be  connected,  so  may  a 
number  of  thermo  electric  pairs,  the  arrangement  being  shown  in 
Fig.  209. 

414.  The  Thermo-electric  Pile.  —  Several 
thermo-electric  pairs,  generally  five,  six,  or  seven,  are 
arranged  in  a  vertical  series,  as  shown  in  Fig.  209,  the 
intervening  spaces  being  much  reduced,  the  successive 
bars  separated  by  strips  of  varnished  paper  only,  and  the 
wire  connection  omitted.  A  similar  series  may  be  united 

to  this  by  soldering  the  free  end 
of  the  antimony  bar  of  one  series 
to  the  free  end  of  the  bismuth 
bar  of  the  other,  the  two  series 
being  separated  by  a  strip  of 
varnished  paper.  Any  desirable 
number  of  such  series  may  be 
thus  united,  compactly  insulated, 
and  set  in  a  metal  frame  so  that 
only  the  soldered  ends  are  open 
to  view.  The  free  end  of  the 
antimony  bar,  representing  the 
-f  electrode,  and  the  free  end  of 

the  bismuth  bar,  representing  the  —  electrode,  are  con- 
nected with  binding  screws,  which  may  be  connected  with 
a  galvanometer.  The  complete  apparatus,  with  the  addition 
of  conical  reflectors,  is  called  a  thermo-electric  pile  or  mul- 
tiplier. It  is  shown  in  Fig.  210. 

EXEBCISES. 


FIG.  210. 


1.  (a.)  Draw  a  figure  of  a  simple  Voltaic  element.      (&.)    State 
what  is  meant  by  the  electric  current,     (e.)    Indicate,    upon   the 


VOLTAIC  ELECTRICITY.  263 

figure,  the  direction  of  the  current,    (d.)  What  are  the  electrodes  ? 
(e.)  Indicate  them  by  their  proper  signs  upon  the  figure. 

2.  (a.)  Describe  or  figure  a  high  resistance  battery  of  Grove's  ele- 
ments.    (&.)  A  low  resistance  battery  of  Bunsen's  elements,     (c.) 
What  is  the  peculiar  advantage  of  the  Daniell's  battery  ? 

3.  (a.)  Describe  an  experiment  illustrating  the  heating  effects  of 
current  electricity.    (6.)  Describe  the  Voltaic  arc. 

4.  (a.)  How  may  a  very  feeble  current  be  detected  ?    (&.)  Describe 
the  apparatus  used,    (c.)  Mention  the  features  contributing  to  its 
delicacy. 

5.  (a.)  How  may  a  fire  poker  be  temporarily  magnetized  with  a 
magnet  ?    (&.)  Without  a  magnet  ?    (c.)  When  temporarily  magnet- 
ized without  a  magnet,  what  kind  of  a  magnet  does  the  pokei 
become  ?    (d .)  State  the  principle  of  the  electric  telegraph. 

6.  (a.)  How  may  an  electric  current  be  induced  ?    (b.)  What  about 
the  continuity  of  an  induced  current?    (c.)  Show  how  a  magnet 
may  produce  the  same  effect  as  an  electric  current,     (d.)  Dees  this 
show  that  there  is  a  fundamental  connection  between  magnetism 
and  electricity  ?    (e.)  Do  the  theories  of  magnetism  and  electricity 
connect  satisfactorily  the  phenomena  of  magnetism  and  electricity ! 

7.  («.)  What  have  we  to  show  that  there  really  is  a  fundamental 
connection  between  heat  and  electricity  ?    (&.)  Compare  the  Leyden 
battery,  the  Voltaic  battery,  and  the  lightning-flash  with  reference 
to  their  effects. 

8.  (a.)  Define  electrolyte.    (&.)  What  term  is  applied  to  chemical 
decomposition  when  effected  by  means  of  an  electric  current  ?    (c.) 
How  would  you  go  about  the  task  of  determining  for  yourself  the 
electro  chemical  nature  of  a  substance  ? 


Recapitulation. — In  this  section  we  have  studied 
Electricity  as  produced  by  Chemical  Action ;  the 
Electric  Current  and  Circuit,  and  Electrodes; 
Voltaic  Batteries;  Amalgamating  Battery 
Zincs ;  the  Thermal  and  Luminous  Effects 
of  current  Electricity,  including  the  Electric  Light ; 
the  deflection  of  the  magnetic  needle  and  the  Galvan- 
ometer ;  Electro-Magnets  and  the  Telegraph  ; 
Electrolysis ;  Electro-plating,  and  Electro- 
typing;  the  Physiological  effects;  Induced  cur- 


264  REVIEW. 

rents;  the  inductive  effect  of  a  Change  of  Distance 
of  the  inducing  current;  electric  currents  Induced 
by  Magnets  ;  Ruhmkorff  s  Coil ;  and  the 
Thermo-electric  pile. 

REVIEW  QUESTIONS  AND  EXEECISES. 

1.  («.)  Give  the  laws  for  pressure  of  liquids,  and  (&.)  explain  each 
by  some  fact  or  experiment. 

2.  (a.)  What  is  a  natural  magnet?     (&.)  An  artificial  magnet? 
(c.)  How  does  a  magnet  behave  toward  soft  iron  ?    (d.)  How  one 
magnet  toward  another  magnet  ? 

3.  Give  the  facts  in  regard  to  the  variation  of  the  magnetic  needle. 

4.  (a.)  What  are  conductors  in  electricity?     (&.)    In  what  two 
ways  may  electrical  separation  be  effected  ? 

5.  («.)    What  conditions  in  the    construction  and  erection  of 
lightning-rods,  are  necessary  to  insure  safety  from  lightning?    (6.) 
Give  the  elements  of  a  simple  Galvanic  cell,  and  (c.)  the  electric 
condition  of  those  elements  within  and  without  the  cell. 

6.  (a.)  A  body  weighs  at  the  surface  of  the  earth  1014  Ibs.;  what 
would  it  weigh  1200  miles  above  the  surface  ?    (&.)  Give  the  velocity 
of  water  issuing  from  an  orifice,  under  a  head  of  81  feet,    (c.)  If 
5  quarts  of  water  weigh  as  much  as  7  of   alcohol,  what  is  the 
specific  gravity  of  the  alcohol  ? 

7.  Find  the  kinetic  energy  of  a  25  Ib.  ball  that  has  fallen  3600  feet 
in  vacuo. 

8.  Give  the  fundamental  principle  of  Mechanics,  and  illustrate 
its  application  by  one  of  the  mechanical  powers. 

9.  (a.)  Over  how  high  a  ridge  can  you  carry  water  in  a  siphon,  where 
the  minimum  range  of  the  barometer  is  27  inches  ?    (&.)  Explain. 

10.  (a.)  What  is  Specific  Gravity?    (6.)  How  do  you  find  that  of 
solids  ?    (c.)  What  principle  is  involved  in  your  method  ? 

11.  (a.)  How  much  water  per  hour  will  be  delivered  from  an 
orifice  of  2  inches  area,  25  feet  below  the  surface  of  a  tank  kept  full 
of  water,  not  allowing  for  resistance  ?    (6.)  Give  the  law  of  magnetic 
attraction  and  repulsion. 

12.  (a.)  State  what  you  have  been  taught  concerning  the  dipping 
needle.    (6.)  Define  and  illustrate  magnetic  induction. 

13.  (a.)  Give  the  law  of   electric  attraction  and  repulsion,  and 
illustrate  by  the  pith-ball  electroscope.     (&.)  Define  conductors  and 
non-conductors,  electrics  and  non-electrics,     (c.)   Illustrate  by  an 
example  of  each. 


REVIEW.  265 

14.  (a.)   Explain  (by  figures)  electric  induction,      (b.)   Explain 
the  charging  of  a  Ley  den  jar.     (c,)  When  charged,  what  is  the 
electric  condition  of  the  outside  and  inside  of  the  jar  ? 

15.  (a.)  Give  the  sources  of  atmospheric  electricity,  and  (6.)  the 
effects  of  lightning. 

16.  (a.)  What  is  the  effect  of  breaking  a  magnet  ?     (&.)  Give  a 
theory  of  magnetism  that  is  competent  to  account  for  the  properties 
of  magnets,  broken  or  unbroken. 

17.  (a.)  How  do  soft  iron  and  tempered  steel  differ  as  to  suscep- 
tibility to  magnetism  ?    (b.)  Describe  one  method  of  magnetizing  a 
steel  bar. 

18.  The  influence  of  the  earth's  magnetism  upon  a  magnetic 
needle  is  merely  directive,     (a.)  Explain  what  this  means,    (ft.) 
Show  why  it  is  so. 

19.  (a.)  What  is  meant  by  electromotive  force?    (b.)  Describe 
Grove's  battery  and  its  mode  of  action,    (c.)  Why  are  battery  zincs 
generally  amalgamated  ? 

20.  (a.)  Describe  Oersted's  apparatus,  and  (&.)  tell  what  its  use 
teaches,    (c. )  Describe  the  construction  of  the  astatic  galvanometer. 

21.  (a.)  Describe  an  electro-magnet,  and  (b.)  tell  what  its  advan- 
tages are.    (c.)  State  the  principle  of  the  electric  telegraph. 

22.  (a.)  Describe  a  Ruhmkorff's  coil,  and  (6.)  explain  its  action. 

23.  (a.)  Define  electrolysis  and  electrolyte.     (6.)  Describe  the  elec- 
trolysis of  water,     (c.)  Give  a  clear  account  of  some  branch  of 
electro-metallurgy,    (d.)  What  is  meant  by  the  terms  electro-positive 
and  electro-negative  ?     ;  s  .?••• 

24.  (a.)  Define  physics.     (&.)  Name  and  define  the  three  conditions 
of  matter,    (c.)  What  do  you  understand  by  energy  ?    (d.)  Explain 
what  is  meant  by  foot-pound. 

25.  (a.)  What  condition  of  the  atmosphere  is  desirable  for  experi- 
ments in  frictional  electricity?     (&.)   Why?    (c.)   How  could  you 
show,  experimentally,  that  there  are  two  opposite  kinds  of  elec- 
tricity ? 

26.  («.)  Describe  the  experiment  with  Faraday's  bag,  and  (6.) 
state  what  it  teaches,     (c.)  Describe  the  dielectric  machine,  and  (d.) 
explain  its  action. 

27.  In  an  air-pump,  the  capacity  of  the  cylinder  is  one-fourth 
that  of  the  receiver.     Under  ordinary  atmospheric  conditions,  both 
together  contain  62  grains  of  air.     Find  the  capacity  (a.)  of  the 
receiver,  (&.)  of  the  cylinder.    After  5  strokes  of  the  piston,  (c.)  how 
many  grains  of  air  would  be  left  in  the  receiver  ?    What  would  be 
its  tension  (d.)  in  pounds  per  square  inch?    (e.)  In  Kg.  per  sq.  cm.? 
(/.)  In  inches  of  mercury  ? 

12 


266  REVIEW. 

28.  (a.)  Supposing  we  have  two  Leyden  jars,  one  charged  on  the 
inside  with  positive  electricity,  and  the  other  with  negative  on  the 
inside  ;  the  two  jars  being  insulated,  can  the  jars  be  discharged  by 
connecting  the  inner  coats  ?    (&.)  Give  reasons  for  your  answer. 

29.  In  a  vessel  having  the  dimensions  of  a  cubic  foot,  sulphuric 
acid  (sp.  gr.  —  1.83)  stands  eight  inches  high  ;  give  the  pressure  on 
the  bottom  and  each  side. 

30.  The  lever  of  a  hydrostatic  press  is  six  feet  long,  the  fulcrum 
being  at  the  end,  and  one  foot  from  the  piston  rod.     The  diameter 
of  the  tube  is  one  inch  ;  that  of  the  cylinder  ten  inches.     The  power 
is  25  Ibs. ;  give  the  effect.    (See  Appendix  A.) 

31.  What  would  a  cubic  foot  of  coal  (sp.  gr.  =  2.4)  weigh  in  a 
solution  of  potash  (sp.  gr.  =  1.2)? 

32.  (a.)  Define  equilibrium  and  its  kinds.    (&.)  Give  examples. 
(c.)  How  does  the  centre  of  gravity  of  any  system,  acted  upon  by 
an  exterior  force,  move  ?    (d.)  Give  an  example. 

33.  (a.)  Figure  a  simple  barometer.    (&.)  Explain  why  the  mer- 
cury stands  above  its  level,    (c.)  What  atmospheric  pressure  will 
sustain  a  column  of  mercury  24  inches  high  ? 

34.  (a.)  How  is  it  proved  that  air  has  weight?    (b.)  What  is  the 
weight  of  air  in  a  room  30  ft.  long,  20  ft.  wide  and  10  ft.  high  ? 

35.  When  a  1000  gram  flask,  containing  700  g.  of  water,  was 
filled  with  the  fragments  of  a  mineral,  it  weighed   1450  g.      Give 
the  specific  gravity  of  the  mineral. 

36.  A  tank  measuring  1  metre  each  way  is  filled  with  water  :  what 
will  be  the  pressure  on  the  bottom  and  sides  ? 

37.  (a.)  What  is  meant  by  kinetic  energy?    (6.)  By  potential 
energy  ? 

38.  Two  inelastic  bodies  are  moving  in  opposite  directions,  one 
weighing  31  grams  and  having  a  velocity  of  24  meters  per  second, 
the  other  weighing  22  grams  and  having  a  velocity  of  18  meters 
per  second:  what  is  the  united  energy  (a.)  before,  and  (6.)  after- 
impact  ? 

89.  Regarding  the  same  bodies  as  moving  in  the  same  direction, 
what  would  be  the  energy  (a.)  before,  and  (&.)  after  impact  ? 

40.  (a.)  Draw  a  simple  figure  showing  the  essential  parts  of  an 
air  pump,  and  (6.)  explain  the  process  of  forming  a  vacuum,     (c.)  If 
the  capacity  of  the  barrel  be  \  that  of  the  receiver,  how  much  air 
will  remain  in  the  receiver  at  the  end  of  the  fourth  stroke  of  the 
piston?  and  (d.}  what  would  be  its  elastic  force  compared  with  that 
of  the  external  air  ? 

41.  Discuss  briefly  the  connection  between  electric  separation  and 
the  more  ordinary  forms  of  energy. 


R  VII. 

\» 


SOUND. 


ECTION  I. 


NATURE,  REFRACTION  AND  REFLECTION 
OF  SOUND. 

415.  Definition  of  Sound.— Sound  is  that  mode 
of  motion  which  is  capable  of  affecting  the  auditory 
nerve. 

(a.)  The  word  sound  is  used  in  two  different  senses.  It  IK  often 
used  to  designate  a  sensation  caused  by  waves  of  air  beating  upon 
the  organ  of  hearing ;  it  is  also  used  to  designate  these  aerial  waves 
themselves.  The  former  meaning  refers  to  a  physiological  or 
psychological  process  ;  the  latter  to  a  physical  phenomenon.  If 
every  living  creature  were  deaf  there  could  be  no  sound  in  the 
former  sense,  while  in  the  latter  sense  the  sound  would  exist  but 
would  be  unheard.  The  definition  above  considers  sound  in  the 
physical  sense  only. 

416.  Undulations.  —  In  beginning  the  study  of 
acoustics,  it  is  very  important  to  acquire  a  clear  idea  of 
the  nature  of  undulatory  motion.    When  a  person  sees 
waves  approaching  the  shore  of  a  lake  or  ocean,  there 
arises  the  idea  of  an  onward  movement  of  great  masses  of 
water.    But  if  the  observer  give  his  attention  to  a  piece  of 
wood  floating  upon  the  water,  he  will  notice  that  it  merely 


268  NATURE  OF  SOUND. 

rises  and  falls  without  approaching  the  shore.  He  may 
thus  be  enabled  to  correct  his  erroneous  idea  of  the  onward 
motion  of  the  water.  Again,  he  may  stand  beside  a  field 
of  ripening  grain,  and,  as  the  breezes  blow,  he  will  see  a 
series  of  waves  pass  before  him.  But  if  he  reflect  and 
observe  carefully,  he  will  see  clearly  that  there  is  no  move- 
ment of  matter  from  one  side  of  the  field  to  the  other ;  the 
grain-ladened  stalks  merely  bow  and  raise  their  heads. 
Most  persons  are  familiar  with  similar  wave  movements  in 
ropes,  chains  and  carpets.  Each  material  particle  has 
a  motion,  but  that  motion  is  vibratory,  not  progres- 
sive. The  only  thing  that  has  an  onward  movement 
is  the  pulse  or  wave,  which  is  only  a  form  or  change 
in  the  relative  positions  of  the  particles  of  the  un- 
dulating substance. 

(a.)  The  motion  of  the  wave  must  be  clearly  distinguished  from 
the  motion  of  particles  which  constitute  the  wave.  The  wave  may 
travel  to  a  great  distance  ;  the  journey  of  the  individual  particle  is 
very  limited. 

417.  Wave  Period. — When  a  medium  is  traversed 
by  a  series  of  similar  waves,  each  particle  is  in  a  state  of 
continued   vibration.    These   vibrations    are    alike,  they 
being  as  truly  isochronous  (§  143)  as  those  of  the  pen- 
dulum.    The  time  required  for  a  complete   vibra- 
tion  is  called   the   period,  and    is    the  same   for 
all  the  particles. 

418.  Wave  Length.— In  such  a  series  of  similar 
waves,  measuring  in  the  direction  in  which  the  waves  are 
travelling,  the  distance  from  any  vibrating  particle  to 
the  next  particle  that  is  in  the  same  relative  posi- 
tion or  "phase"  is  called  a  wave  length.    In  the  case 


NATURE   OF  SOUND. 


269 


of  water  waves,  for  example,  the  horizontal  distance  from 
one  crest  to  the  next  crest  would  be  a  wave  length. 

419.  Amplitude. — Amplitude  means  the  dis- 
tance between  the  extreme  positions  of  the  vibrating 
particle,  or  the  length  of  its  journey.    As  in  the  case  of 
the  pendulum,  amplitude  and  period  are  independent  of 
each  other.    Amplitude  is  also  independent  of  wave  length. 

420.  Relation  of  Period,  Wave  Length  and 
Velocity. — During  one  period  there  will  be  one  com- 
plete vibration,  and  the  wave  will  advance  one  wave  length. 
The  velocity  of  the  wave  may  be  found  by  multiplying  the 
wave  length  by  the  number  of  vibrations  per  second. 
Conversely,  the  wave  length  may  be  found  by  divide 
ing  the  velocity  by  the  number  of  vibrations. 

421.  Cause  of  Sound. — All  sound  may  be  traced 
to  the  vibrations  of  some  material  body.     When  a 

bell  is  struck,  the  edges  of  the 
bell  are  set  in  rapid  vibration, 
as  may  be  seen  by  holding  a 
card  or  finger  nail  lightly  upon 
the  edge.  The  particles  of  the 
bell  strike  the  adjacent  parti- 
cles of  air,  these  pass  the 
motion  thus  received  on  to  the 
air  particles  next  beyond,  and 
these  to  those  beyond. 

(a.)  That  sound  is  due  to  vibra- 
tory motion  may  be  shown  by  nu- 
merous experiments.     Holding  one 
end  of  a  straight  spring,  as  a  hick- 
FIG.  211.  ory  stick,  in  a  vise,  pull  the  free 


J>'  D   D" 


270  NATURE  OF  SOUND. 

end  to  one  side  and  let  it  go.  Elasticity  will  return  it  to  its  position 
of  rest,  kinetic  energy  will  carry  it  beyond,  and  so  on,  a  vibratory 
motion  being  thus  produced.  When  the  spring  is  long,  the  vibra- 
tions may  be  seen.  By  lowering  the  spring  in  the  vise,  the  vibrating 
part  is  shortened,  the  vibrations  reduced  in  amplitude  and  increased 
in  rapidity.  As  the  spring  is  shortened,  the  vibrations  become 
invisible  but  audible,  showing  that  a  sufficiently  rapid  vibratory 
motion  may  produce  a  sound. 

(b.)  Suspend  a  pith  ball  by  a  thread  so  that  it  shall  hang  lightly 
against  one  prong  of  a  tuning-fork.  When  the  fork  is  sounded,  the 
pith  ball  will  be  thrown  off  by  the  vibrations  of  the  prongs.  Other 
illustrations  of  the  same  truth  will  be  observed  as  we  go  on. 

(c.)  The  vibrations  of  a  tuning-fork  may  be  made  visible  in  the 
following  manner :  A  glass  plate  which  has  been  blackened  by 
holding  it  in  a  petroleum  flame  is  arranged  so  as  to  slide  easily  in 
the  grooved  frame  F.  A  pointed  piece  of  metal  is  attached  to  one 


FIG.  212. 

of  the  prongs  of  the  fork.  When  the  fork  is  made  to  vibrate,  the 
point  placed  against  the  smoked  plate  and  the  plate  drawn  along 
rapidly  in  the  grooves,  the  point  traces  on  the  glass  an  undulating 
line  which  represents  fairly  the  vibratory  movement  of  the  prong. 

422.  Propagation  of  Sound. — Sound  is  ordi- 
narily propagated  through  the  air.  Tracing  the  sound 
from  its  source  to  the  ear  of  the  hearer,  we  may  say  that 
the  first  layer  of  air  is  struck  by  the  vibrating  body.  The 
particles  of  this  layer  give  their  motion  to  the  particles  of 
the  next  layer,  and  so  on  until  the  particles  of  the  last 
layer  strike  upon  the  drum  of  the  ear. 

(a.)  This  idea  is  beautifully  illustrated  by  Prof.  Tyndall.     He 


NATURE  OF  SOUND. 


271 


imagines  five  boys  placed  in  a  row  as  shown  in  Fig.  213.     "  I  sud- 

denly push  A  ;  A  pushes  B  and  regains  his  upright  position  ;  B 

pushes  C  ',   G  pushes 

D;    D   pushes    E  ;  0 

each    boy   after   the 

transmission  of   the 

push,  becoming  him- 

self erect.     E,  hav- 

ing nobody  in  front, 

is   thrown   forward. 

Had  he  been  stand- 

ing on  the  edge  of 

a  precipice  he  would 

have  fallen  over;  had 

he  stood  in  contact 


FIG  213. 


with  a  window,  he  would  have  broken  the  glass  ;  had  he  been  close 
to  a  drum-head,  he  would  have  shaken  the  drum.  We  could  thus 
transmit  a  push  through  a  row  of  a  hundred  boys,  each  particular 
boy,  however,  only  swaying  to  and  fro.  Thus  also  we  send  sound 
through  the  air,  and  shake  the  drum  of  a  distant  ear,  while  each 
particular  particle  of  the  air  concerned  in  the  transmission  of  the 
pulse  makes  only  a  small  oscillation." 

423.  Sound  Waves.—  The  layers  of  air  are  crowded 
more  closely  together  by  each  outward  vibration  of  the 


FIG.  214. 

sounding  body;  a  condensation  of  the  air  is  thus  produced 
As  the  sonorous  body  vibrates  in  the  opposite  direction, 


272 


NATURE  OF  SOUND. 


the  nearest  layer  of  air  particles  follows  it ;  a  rarefaction 
of  the  air  is  thus  produced,  A  sound  wave,  therefore, 
consists  of  two  parts,  a  condensation  and  a  rarefac- 
tion. The  motion  of  any  air  particle  is  backward  and 
forward  in  the  line  of  propagation,  and  not  "  up  and  down  " 
across  that  line,  as  in  the  case  of  water  waves.  A  series  of 
complete  sound  waves  consists  of  alternate  condensations 
and  rarefactions  in  the  form  of  continually  increasing 
spherical  shells,  at  the  common  centre  of  which  is  the 
sounding  body.  Any  line  of  propagation  of  the  sound 
would  be  a  radius  of  the  sphere. 

424.  Sound  Media. — The  air  particles  impart  their 
motion  to  other  particles  because  of  their  elasticity.  Any 
elastic  substance  may  become  the  medium  for  the 
transmission  of  sound,  but  such  a  medium  is  neces- 
sary. The  elasticity  of  a  body 
may  be  measured  by  the  re- 
sistance it  opposes  to  compres- 
sion. The  less  the  compres- 
sibility, the 
greater  the 
elasticity. 


FIG.  215. 


(a.)  That  sound 
is  not  transmit- 
ted in  a  vacuum 
is  shown  as  fol- 

lows:  A  lar£e 

glass  globe,  pro- 
vided with  a  stop-cock,  contains  a 
small  bell  suspended  by  a  thread. 
When  the  air  is  pumped  from  the 
globe  and  the  globe  shaken,  no 
sound  is  heard,  although  the  clap- 
per of  the  bell  is  seen  to  strike 


FIG.  216. 


NATURE  OF  SOUND.  273 

against  the  bell.    Readmitting  the  air,  and  again  shaking  the  globe, 
the  sound  is  plainly  heard.    (See  Fig.  215.) 

(6.)  A  small  music  box,  or  a  clock-work  arrangement  for  striking 
a  bell  (Fig.  216),  may  be  supported  upon  a  thick  cushion  of  felt  or 
cotton-batting,  and  placed  under  the  capped  receiver  of  an  air-pump. 
When  the  receiver  is  exhausted,  and  the  machinery  started  by  the 
rod  g,  the  motion  may  be  seen  but  hardly  any  sound  will  be  heard. 
If  the  support  were  perfectly  inelastic  and  the  exhaustion  complete, 
no  sound  would  be  audible.  The  experiment  may  be  made  more 
perfect  by  filling  the  exhausted  receiver  with  hydrogen  and  again 
exhausting  the  gas. 

425.  Velocity  of  Sound  ill  Air. — It  is  a  familiau 
fact  that  the  transmission  of  sound  is  not  instantaneous. 
The  blow  of  a  hammer  is  often  seen  several  seconds  before 
the  consequent  sound  is  heard ;  steam  escaping  from  the 
whistle  of  a  distant  locomotive  becomes  visible  before  the 
shrill  scream  is  audible;  the  lightning  precedes  the  thunder. 
As  we  shall  see  further  on,  the  time  required  for  the 
propagation  of  light  through  terrestrial  distances  is  inap- 
preciable.   Hence  the  interval  between  the  two  sensations 
of  seeing  and  hearing  is  required  for  the  transmission  of 
the  sound.    This  interval  being  observed  and  the  distance 
being  known,  the  velocity  is  easily  computed.     By  such 
means  it  has  been  found  that  the  velocity  of  sound  in 
air  at  the  freezing  temperature  is  about  332  m.,  or 
1090  ft.  per  second.    There  is  some  reason  for  believing 
that  very  loud  sounds  travel  somewhat  more  rapidly  than 
sounds  of  ordinary  loud  ness.     With  this  exception  it  may 
be  said  that,  in  a  given  medium,  all  sounds  travel  with  the 
same  velocity. 

426.  Velocity  in  Other  Media.— The  velocity 
of    sound    depends    upon    two    considerations — the 
elasticity  and  the  density  of  the  medium.    It  varies 
directly  as  the  square  root  of  the  elasticity,  and 


274  NATURE  OF  SOUND. 

Inversely  as  the  square  root  of  the  density.  At  the 
freezing  temperature,  sound  travels  through  oxygen  with  a 
velocity  of  1040  feet,  and  through  hydrogen  with  a  velocity 
of  4164  feet  per  second. 


(a.)  It  is  a  very  common  mistake  to  think  that  an  increase  of 
density  causes  an  increase  of  velocity.  It  is  known,  e.g.,  that  sound 
travels  more  rapidly  in  water  than  in  air  ;  that  water  is  more  dense 
than  air  ;  hence,  say  the  superficial,  sound  travels  most  rapidly  in 
the  densest  bodies.  It  does  not  follow.  Other  things  being  equal, 
the  denser  the  medium,  the  less  the  velocity  of  the  motion.  A  little 
reflection  will  show  that  this  must  be  so  ;  experiments  will  verify 
the  conclusion.  In  wave  motion,  the  particles  of  the  medium  con- 
stitute the  thing  that  is  moved.  With  a  given  expenditure  of  energy, 
a  number  of  light  particles  is  moved  more  rapidly  than  an  equal 
number  of  heavy  particles  (§  157). 

427.  Effect  of  Temperature  Upon  Velocity. 

—  An  increase  of  the  temperature  of  the  air  increases  its 
elasticity  and  decreases  its  density.  We  might,  therefore, 
expect  sound  to  travel  more  rapidly  in  warm  than  in  cold 
air.  Experiment  confirms  the  conclusion.  Tliere  is  an 
added  velocity  of  about  1.12  feet  for  every  Fah- 
renheit degree,  or  of  about  2  feet  for  every  centi- 
grade degree  of  increase  of  temperature.  (The 
freezing  temperature  is  32°  F,  or  0°  C.) 

428.  Noise.  —  A  noise  may  be  momentary  or  con- 
tinuous.    A  momentary  noise  consists  of  a  single  pulse  in 
the  medium  produced  by  a  single  and  sudden  blow.     It 
has  neither  period  nor  wave  length.    A  continuous  noise 
consists  of  an  irregular  and  rapid  succession  of  pulses. 
The  ear  is  so  constructed  that  its  vibrations  disappear  very 
rapidly,  but  the  disappearance  is  not  instantaneous  ;  if  the 


NATURE   OF  SOUND.  275 

motion  imparted  to  the  auditory  nerve  by  each  individual 
pulse  of  the  series  continue  until  the  arrival  of  its  suc- 
cessor, the  sound  will  not  cease  at  all.  TJiat  the  sound 
may  be  mere  noise,  the  pulses  must  be  irregular  in 
their  recurrence.  > 

(a.)  Momentary  noises  may  be  produced  by  pounding  with  a 
hammer,  stamping  with  the  foot,  clapping  the  hands,  or  drawing  a 
stick  slowly  along  the  pickets  of  a  fence.  Continuous  noises  may 
be  produced  by  sawing  boards  or  filing  saws.  They  are  more  or 
less  familiar  in  the  rattling  of  wheels  over  a  stony  pavement,  the 
roar  of  waves,  or  the  crackling  of  a  large  fire. 

429.  Music. — «/£   musical  sound  consists    of  a 
regular  and  rapid  succession  of  pulses.    The  regu- 
larity of  the  succession  renders  the  sound  smooth  and 
agreeable  ;  the  rapidity  renders  it  continuous.    To  secure 
this  smoothness  the  pulses  must  be  perfectly  periodic ;  the 
sounding  body  must  vibrate  with  the  unerring  regularity 
of  the  pendulum,  but  impart  much  sharper  and  quicker 
shocks  to  the  air.     Every  musical  sound  has  a  well-defined 
period  and  wave  length. 

430.  Elements  of  Musical  Sounds.— Musical  sounds  or 
tones  have  three  elements — intensity  or  loudness,  pitch,  and  timbre 
or  quality.    The  first  two  of  these  we  shall  consider  at  once,  the 
third,  a  little  further  on. 

431.  Intensity  and  Amplitude. — Intensity  or 
loudness  of  sound  depends  upon  the  amplitude  of 
vibration.     The  greater  the  amplitude,  the  louder  the 
sound. 

(a.)  If  the  middle  of  a  tightly-stretched  cord  or  wire,  as  a  guitar 
string,  b3  drawn  aside  from  its  position  of  rest  and  then  set  free,  it 
will  vibrate  to  and  fro  across  its  place  of  rest,  striking  the  air  and 
sending  sound  waves  to  the  ear.  If  the  middle  of  the  string  be 
drawn  aside  to  a  greater  distance  and  then  set  free,  the  swing  to 
and  fro  will  be  increased,  harder  blows  will  be  struck  upon  the  air. 


276 


NATURE  OF  SOUND. 


and  the  air  particles  will  move  forward  and  backward  through  a 
greater  distance.  In  other  words,  the  amplitude  of  vibration  has 
been  increased.  But  this  change  in  the  aerial  wave  produces  a 
change  in  the  sensation.  We  still  recognize  the  pitch  to  be  the 
same  as  before  ;  the  tone  is  neither  higher  nor  lower.  We  even 
recognize  it  still  as  being  produced  by  a  guitar  string.  The  only 
difference  is  that  the  sensation  is  more  intense ;  we  say  that  the 
sound  is  louder. 

432.  Intensity  and  Distance. — The  intensity 
of  sound  varies  inversely  as  the  square  of  the  dis- 
tance from  the  sounding  body.  Hence,  the  distance 
to  which  a  sound  may  be  heard  depends  upon  its  intensity. 

I 


FIG.  217. 

433»  Acoustic  Tubes. — If  the  sound  wave  be  not 
allowed  to  expand  as  a  spherical  shell,  the  energy  of  the 
wave  cannot  be  diffused.  This  means  that  its  intensity 
will  be  maintained.  In  acoustic  tubes  (Fig.  217)  this 
diffusion  is  prevented ;  the  waves  are  propagated  in 


NATURE   OF  SOUND.  277 

only  one  direction.  In  this  way,  sound  may  be  trans- 
mitted to  great  distances  without  considerable  loss  of 
intensity. 

434.  Pitch. — The  second  element  of  a  musical  sound 
is  pitch,  by  which  we  mean  the  quality  that  constitutes 
the  difference  between  a  low  or  grave  tone  and  a  high 
tone.     All  persons  are  more  or  less  able   to  recognize 
differences  in  pitch.     A  person  who   is  able  to  judge 
accurately  of  the  pitch  of  sounds  is  said  to  have  a  "  good 
ear  for  music."     The  pitch  of  a  sound  depends  upon 
the  rapidity  of  vibration  of  the    sounding   body, 
or,  in  other  words,  upon  the  rate  at  which  sound  pulses 
follow  each  other.     The  more  rapid  the  vibrations,  the 
higher  the  tone. 

435.  Experimental  Proof  of  the  Cause  of 
Pitch.  —  That    pitch    depends    upon 

rapidity  of  vibration,  may  be  roughly 

shown  by  drawing  the  finger  nail  across 

the  teeth  of  a  comb,  slowly  the  first  time 

and  rapidly  the  second  time.    It  may  be 

shown  more  satisfactorily  by  means  of 

Savart's  wheel,  shown  in  Fig.  218.    This 

consists  of  a  heavy  brass  ratchet-wheel, 

supported  on  an  iron  frame  and  pedestal.     The  wheel  may 

be  set  in  rapid  revolution  by  a  cord  wound  around  the  axis. 

By  holding  a  card  against  the  teeth,  when  in  rapid  motion, 

a  shrill  tone  will  be  produced,  gradually  falling  in  pitch  as 

the  speed  is  lessened. 

(a.)  If  the  sounding  body  and  the  listening  ear  approach  each 
other,  the  sound  waves  will  beat  upon  the  ear  with  greater  rapidity. 
This  is  equivalent  to  increasing  the  rapidity  of  vibration  of  the 


278  NATURE.  OF  SOUXD. 

sounding  body.  The  opposite  holds  true  when  the  sounding  body 
and  the  ear  recede  from  each  other.  This  explains  why  the  pitch 
of  the  whistle  of  a  railway  locomotive  is  perceptibly  higher  when 
the  train  is  rapidly  approaching  the  observer,  than  when  it  is  rapidly 
moving  away  from  him. 

436.  Relation  between  Pitch  and  Period.— 

Rate  of  vibration  and  period  are  reciprocals.  If  the 
rate  of  vibration  be  256  per  second,  the  period  is  ^  of  a 
second.  The  period  may,  therefore,  be  used  to  measure 
the  pitch ;  the  greater  the  period,  the  lower  the  pitch. 

437.  Relation    between   Pitch   and  Wave 
Length. — Since,  in  a  given  medium,  all  sounds  travel 
with  the  same  velocity,  the  rate  of  vibration  determines 
the  wave  length.    If  the  sounding  body  vibrate  224  times 
per  second,  224  waves  will  be  started  each  second.     If  the 
velocity  of  the  sound  be  1120  feet,  the  total  length  of  these 
224  waves  must  be  1120  feet,  or  the  length  of  each  wave 
must  be  five  feet.    If  another  body  vibrate  twice  as  fast, 
it  will  crowd  twice  as  many  waves  into  the  1120  feet;  each 
wave  will  be  only  two  and  a  half  feet  long.    Thus  wave 
length  may  be  used  to  measure  the  pitch — the  greater  the 
wave  length,  the  lower  the  pitch. 

438.  Refraction  of  Sound.— We  have  a  clear 
idea  of  sound  waves  advancing  as  concentric,  spherical 
shells,  but  we  are  far  more  familiar  with  the  idea  of  sound 
advancing  in  definite  straight  lines.     This  idea  is  also  cor- 
rect, the  lines  being  radii  of  the  sphere.    We  may  thus 
speak  of  lines  or  "rays"  of  sound,  meaning  thereby  the 
direction  in  which  the  sonorous  pulses  are  propagated. 
The  ray  is  necessarily  perpendicular  to  the  wave.    When 
the  noise  of  the  street  is  heard  by  a  person  in  a  closed  room, 
the  sound  must  have  passed  from  the  air  without  to  the 


NATURE   OF  SOUXD. 


279 


solid  matter  of  the  walls,  and  from  this  to  the  air  within. 
When  sound  thus  passes  obliquely  from  one  medium  to 
another,  the  rays  are  bent.  Tills  bending  of  a  sound 
ray  is  called  refraction  of  sound. 

439.  A  Sound  Focus.— Ordinarily,  sound  rays  are 
divergent.  The  sound  is  therefore  continually  diminishing 
in  intensity.  By  means  of  their  refrangibility,  they  may 
be  made  convergent.  If  the  divergent  rays  strike  the  side 
of  a  sack  shaped  like  a  double  convex  lens,  made  of  two 
films  of  collodion,  or  very  thin  India  rubber,  and  filled 
with  carbonic  acid  gas  (C02),  their  divergence  will  be  di- 
minished ;  they  may  thus  be  made  parallel,  or  even  con- 
vergent, after  passing  through  the  sack.  At  the  point 
where  these  rays  converge  their  total  energy  will  be  con- 
centrated, and  the  intensity  of  the  sound  be  thus  increased. 
The  point  where  the  refracted  rays  intersect  is  called  the 
focus  of  the  lens.  The  laws  of  refracted  sound  are  the 
same  as  those  of  refracted  light,  to  be  studied  further  on. 

(a.)  If  a  watch  be  hung  near  such  a  refractor,  its  ticking  may  be 
heard  by  placing  the  ear  at  the  focus  on  the  other  side  of  the  sack  ; 
when  the  sack  is  re- 
moved, the  ticking  is 
no  longer  audible.  A 
few  trials  will  enable 
the  experimenter  to 
determine  the  proper 
positions  for  the  watch, 
the  lens  and  the  ear. 
The  refraction  directs 
to  the  ear  all  the  en- 
ergy exerted  upon  the 
anterior  surface  of  the 


FIG.  219. 


sack.  This  energy  is  sufficient  to  excite  the  sensation  of  hearing. 
A  little  reflection  will  show  that  when  the  sack  is  removed,  the 
energy  exerted  upon  the  smaller  surface  of  the  tympanum  at  the 


280  NATURE  OF  SOUND. 

greater  distance  is  very  much  diminished.  This  lesser  energy  is 
unable  to  excite  the  auditory  nerve  to  action,  and  the  ticking  of  the 
watch  is  unheard. 

440.  Reflection  of  Sound. — When  a  sound  ray 
strikes  an  obstacle,  it  is  reflected  in  obedience  to  the  prin- 
ciple given  in  §  97.     This  fact  is  turned  to  account  in  the 
case  of  "conjugate  reflectors"  of  sound.    Fig.  220  repre- 
sents the  section  of  two  parabolic  reflectors  mn  and  op. 
It  is  a  peculiarity  of  such  reflect- 
ors that  rays  starting  from  the         JP 

focus,  as  F,  will  be  reflected  as  >£— 
parallel  rays,  and  that  parallel  rays 
falling  upon  such  a  reflector  will 
converge  at  the  focus,  as  F' . 
Hence,  two  such  reflectors  may 
be  placed  in  such  a  position  that  FlG  22Q 

sound  waves  starting  from  one 

focus  shall,  after  two  reflections,  be  converged  at  the  other 
focus.  Two  reflectors  so  placed  are  said  to  ~be  con- 
jugate to  each  other.  This  principle  underlies  the 
phenomena  of  whispering  galleries. 

(a.)  "  The  great  dome  of  St.  Paul's  Cathedral  in  London  is  so  con- 
structed that  two  persons  at  opposite  points  of  the  internal  gallery, 
placed  in  the  drum  of  the  dome,  can  talk  together  in  a  mere  whisper. 
The  sound  is  transmitted  from  one  to  the  other  by  successive  reflec- 
tions along  the  course  of  the  dome."  A  similar  phenomenon  is 
observable  in  the  dome  of  the  Capitol  at  Washington. 

441.  Experiment. — At  the  focus  of  a  curved  re- 
flector, place  a  watch  or  other  suitable  sounding  body. 
Directly  facing  it,  but  at  a  distance  so  great  that   the 
ticking  is  unheard,  place  a  similar  reflector.     When  the 
ear  is  placed  at  the  focus  of  the  second  mirror,  as  shown  in 
Fig.  221,  the  ticking  is  plainly  heard. 


NATURE  OF  SOUND.  281 


FIG.  221. 

(a.)  In  the  experiment  above  described,  it  is  plain  that  many  of 
the  rays  reflected  by  the  first  mirror  are  intercepted  before  they 
reach  the  second  mirror.  This  may  be  remedied,  in  part,  by  the 
use  of  an  ear-trumpet,  the  larger  end  being  held  at  the  focus  of  the 
second  reflector.  The  ear-trumpet  may  be  a  glass  funnel,  with  a 
piece  of  rubber  tubing  leading  from  its  smaller  end  to  the  ear.  The 
experiment  may  be  modified  by  using  a  single  reflector,  the  watch 
being  placed  a  little  further  from  the  reflector.  The  proper  positions 
for  the  watch  and  the  funnel  are  easily  determined  by  experiment 
They  are  conjugate  foci  (§  602). 

442.  Echo. —  When  a  sound,  after  reflection,  is 
audible,  it  is  called  an  echo.  The  distinctness  with 
which  it  is  heard  depends  upon  the  distance  of  the  ear 
from  the  reflecting  surface.  A  very  quick,  sharp  sound 
may  produce  an  echo  even  when  the  reflecting  surface  is 
not  more  than  fifty  or  sixty  feet  away,  but  for  articulate 
sounds  a  greater  distance  is  necessary. 

(a.)  Few,  if  any,  persons  can  pronounce  distinctly  more  than 
about  five  syllables  in  a  second.  At  the  ordinary  temperature, 
sound  travels  about  1120  feet  per  second.  In  a  fifth  of  that  time 
it  would  travel  about  224  feet.  If,  therefore,  the  reflecting  surface 
be  112  feet  distant,  the  articulate  sound  will  go  and  return  before 
the  next  syllable  is  pronounced.  The  two  sounds  will  not  inter- 
fere, and  the  echo  will  be  distinctly  heard.  If  the  reflecting  sur- 
face be  less  than  this  distance,  the  reflected  sound  will  return  before 


NATURE  OF  SOUND. 


the  articulation  is  complete  and  confusedly  blend  with  it.  If  the 
reflector  be  224  feet  distant,  there  will  be  time  to  pronounce  two 
syllables  before  the  reflected  wave  returns.  The  echo  of  both 
syllables  may  then  be  heard  ;  and  so  on.  The  echo  may  be  heard 
sometimes  when  the  direct  sound  cannot  be  heard. 

(&.)  Suppose  the  speaker  to  stand  1120  feet  from  the  reflecting 
substance.  If  then  he  speak  ten  syllables  in  two  seconds,  the  echo 
of  the  first  will  return  just  as  the  last  is  spoken  ;  the  echo  of  each 
syllable  will  be  distinct.  But  if  he  continues  to  speak,  the  direct 
and  the  reflected  sounds  will  become  blended  and  confused.  The 
reflecting  surface  should  be  a  large,  vertical  wall,  or  similar  object, 
as  a  huge  rock. 

(c.)  When  two  opposite  surfaces,  as  parallel  walls,  successively 
reflect  the  sound,  multiple  echoes  are  heard.  Sometimes  an  echo  is 
thus  repeated  20  or  30  times. 

EXERCISES. 

1.  If  18  seconds  intervene  between  the  flash  and  report  of  a  gun, 
what  is  its  distance,  the  temperature  being  82°  F.? 

2.  What  will  be  the  length  of  the  sound  waves  propagated  through 
air  at  a  temperature  of  15°  C.  by  a  tuning-fork  that  vibrates  224 
times  per  second  ? 

3.  State  clearly  the  difference  between  a  transverse  and  a  longi- 
tudinal wave. 

4.  Determine  the  temperature  of  the  air  when  the  velocity  of 
sound  is  1150  feet  per  second. 

5.  If  A  is  50  m.  from  a  bell,  and  B  is  70  m.  from  it,  how  will  the 
loudness  of  the  sound  as  heard  by  B  compare  with  the  loudness  as 
heard  by  A  ? 

6.  A  shot  is  fired  before  a  cliff,  and  the  echo  heard  in  six  seconds. 
The  temperature  being  15°  C.  find  the  distance  of  the  cliff. 

7.  A   certain  musical  instrument   makes    1100  vibrations    per 
second.    Under  what  conditions  will  the  sound  waves  be  each  a  foot 
long? 

8.  How  many  vibrations  per  second  are  necessary  for  the  forma- 
tion of  sound  waves  four  feet  long,  the  velocity  of  sound  being 
1120  feet  ?    What  will  be  the  temperature  at  the  time  of  the  experi- 
ment? 

9.  Taking  the  velocity  of  sound  as  332  m.,  find  the  length  of  a 
wave  if  there  are  830  vibrations  per  second. 

10.  The  waves  produced  by  a  man's  voice  in  common  conversation 
are  from  eight  to  twelve  feet  long.     If  the  velocity  of  sound  be 


COMPOSITION  OF  SOUND    WAVES.  283 

1128  feet,  find  the  corresponding  numbers  of  vibrations  of  vocal 
chords. 

11.  A  person  stands  before  a  cliff  and  claps  his  hands.  In  f  of  a 
second  he  hears  the  echo.  How  far  distant  was  the  cliff  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Definition  of  sound;  Undulations;  the  Pe- 
riod, Length  and  Amplitude  of  waves ;  the 
Cause  and  Propagation  of  sound  ;  sound  Waves 
and  Media  ;  the  Velocity  in  air  and  in  other  media, 
and  the  effect  of  Temperature;  the  difference  between 
Noise  and  Music ;  the  Three  Elements  of 
musical  sounds ;  the  relation  of  Loudness  to  ampli- 
tude and  distance;  Acoustic  Tubes;  the  cause  of 
differences  in  Pitch  ;  the  relation  that  exists  between 
Pitch  and  Period,  or  Wave  Length ;  Re- 
fraction and  Foci  of  sound;  Reflection  of  sound; 
Echoes. 


./ 

COMPOSITION  OF  SOUND  WAVES;  MUSICAL 
INSTRUMENTS. 

443.  Sympathetic  Vibrations.— The  string  of  a 
violin  may  be  made  to  vibrate  audibly  by  sounding  near 
it  a  tuning-fork  of  the  same  tone.  By  prolonging  a  vocal 
tone  near  a  piano,  one  of  the  wires  seems  to  take  up  the 
note  and  give  it  back  of  its  own  accord.  If  the  tone  be 
changed,  another  wire  will  give  it  back.  In  each  case, 
that  wire  is  excited  to  audible  action,  which  is  able  to 


\  t>  f\  A  ,< 

*"-  or 
TTTsi 


284 


COMPOSITION   OF  SOUND    WAVES. 


vibrate  at  the  same  rate  as  do  the  sonorous  waves  that  set 
it  in  motion.  Thus  the  vibrations  of  the  strings  may  pro- 
duce sonorous  waves,  and  the  waves  in  turn  may  produce 
vibrations  in  another  string.  The  most  important  feature 
of  the  phenomenon  is  that  the  string  absorbs  only  the 
particular  kind  of  vibration  that  it  is  capable  of 
producing.  (Read  Tyndall  "  On  Sound,"  Chap.  IX,  §  4.) 


FIG.  222. 

(«.)  Tune  to  unison  two  strings  upon  the  same  sonometer  (Fig. 
222).  Upon  one  string  place  two  or  three  paper  riders.  With  a 
violin  bow,  set  the  other  string  in  vibration.  The  sympathetic 
vibrations  thus  produced  will  be  shown  by  the  dismounting  of  the 
riders,  whether  the  vibrations  be  audible  or  not.  Change  the  tension 
of  one  of  the  strings,  thus  destroying  tlie  unison.  Repeat  the  experi- 
ment and  notice  that  the  sympathetic  vibrations  are  not  produced. 

(6.)  Place  several  feet  apart  two  tuning-forks  mounted  upon  reso- 
nant cases.  The  forks  should  have  the  same  tone,  and  the  cases 
should  rest  upon  pieces  of  rubber  tubing  to 
prevent  the  transf  errence  of  vibratory  motion  to 
and  through  the  table.  Sound  the  first  fork  by 
rapidly  separating  the  two  prongs  with  a  rod. 
Notice  the  pitch.  At  the  end  of  a  second  or 
two  touch  the  prongs  to  stop  their  motion  and 
sound.  It  will  be  found  that  the  second  fork 
has  been  set  in  motion  by  the  repeated  blows 
of  the  air,  and  is  giving  forth  a  sound  of  the 
same  pitch  as  that  originally  produced  by  the 
first  fork.  Fasten,  by  means  of  wax,  a  3-cent  silver  piece  or  other 
small  weight  to  one  of  the  prongs  of  the  second  fork.  An  attempt 
to  repeat  the  experiment  will  fail. 


FIG.  223. 


COMPOSITION  OF  SOUND    WAVES.  285 

(c.)  When  the  two  forks  are  in  unison,  their  periods  are  the  same. 
The  second  and  subsequent  pulses  sent  out  by  the  first  fork  strike 
the  second  fork,  already  vibrating  from  the  effect  of  the  first  pulse, 
in  the  same  phase  of  vibration,  and  thus  each  adds  its  effect  to  that 
of  all  its  predecessors.  If  the  forks  be  not  in  unison,  their  periods 
will  be  different  and  but  few  of  the  successive  pulses  can  strike 
the  second  fork  in  the  same  phase  of  vibration ;  the  greater  number 
will  strike  it  at  the  wrong  instant. 

444.  Soundiiig-Boards. — In    the    case   of  the 
sonometer,  piano,  violin,  guitar,   etc.,  the  sound  is  due 
more  to  the  vibrations  of  the  resonant  bodies  that  carry 
the  strings  than  to  the  vibrations  of  the  strings  them- 
selves.    The  strings  are  too  thin  to  impart  enough  motion 
to  the  air  to  be  sensible  at  any  considerable  distance ;  but 
as  they  vibrate,  their  tremors  are  carried  by  the  bridges  to 
the  material  of  the  sounding  apparatus  with  which  they 
are  connected. 

(a.)  This  sounding  apparatus  usually  consists  of  thin  pieces  of 
wood  which  are  capable  of  vibrating  in  any  period  within  certain 
limits.  The  vibrations  of  these  large  surfaces  and  of  the  enclosed 
air  produce  the  sonorous  vibrations.  The  excellence  of  a  Cremona 
violin  does  not  lie  in  the  strings,  which  may  have  to  be  replaced 
daily.  The  strings  are  valuable  to  determine  the  rate  of  vito'ation 
that  shall  be  produced  (§  455).  The  excellence  of  the  instrument 
depends  upon  the  sonorous  character  of  the  wood,  which  seems  to 
improve  with  age  and  use. 

(6.)  Similar  remarks  apply  to  the  tuning-fork,  When  a  tuning- 
fork  held  in  the  hand  is  struck,  but  a  feeble  sound  is  heard.  When 
the  handle  is  placed  upon  the  table  or  almost  any  solid  having  a 
considerable  surface,  the  intensity  of  the  sound  is  remarkably  in- 
creased. Hence,  for  class  or  lecture  experiments,  tuning  forks 
should  be  mounted  as  shown  in  Fig.  223. 

Note. — Before  beginning  the  study  of  the  telephone,  the  pupil 
should  carefully  review  §§  408,  409. 

445,  The   Telephone. — This  instrument  is  repre- 
sented in  section   by  Fig.  224.    A   is  a  permanent  bar 


286 


COMPOSITION  OF  SOUND    WAVES. 


FIG.  224. 


magnet,  around  one  end  of  which  is  wound  a  coil,  B,  of 
fine  copper  wire  carefully  insulated.      The  ends  of  this 

coiled  wire  are 
attached  to  the 
larger  wires  CC, 
which  communi- 
cate with  the 
binding  posts 
DD.  In  front  of 
the  magnet  and 
coil  is  the  soft  iron  diaphragm  E,  which  corresponds  to 
the  disc  #,  of  Fig.  203.  The  distance  between  E  and  the 
end  of  A  is  delicately  adjusted  by  the  screw  S.  In  front 
of  the  diaphragm  is  a  wooden  mouth-piece  with  a  hole 
about  the  size  of  a  dime,  at  the  middle  of  the  diaphragm 
and  opposite  the  end  of  the  magnet.  The  outer  case  is  made 
of  wood  or  hard  rubber.  The  external 
appearance  of  the  complete  instrument 
is  represented  by  Fig.  225.  The  bind- 
ing posts  of  one  instrument  being  con- 
nected by  wires  with  the  binding  posts 
of  another  at  a  distance,  conversation 
may  be  carried  on  between  them. 


446.    Action    of   the    Tele- 
phone.— When  the  mouth-piece  is 
brought  before  the  lips  of  a  person  who  I 
is  talking,  air  waves  beat  upon  the  dia- 1 
phragm  and  cause  it  to  vibrate.     The 
nature  of  these  vibrations  depends  upon 
the  loudness,  pitch,  and  timbre  of  the 
sounds  uttered.     Each  vibration  of  the  diaphragm  induces 


FIG.  225. 


COMPOSITION  OF  SOUND    WAVES.  287 

an  electric  current  in  the  wire  of  B.  These  currents  are 
transmitted  to  the  coil  of  the  connected  telephone,  at  a 
distance  of,  perhaps,  several  miles,  and  there  produce,  in 
the  diaphragm  of  the  instrument,  vibrations  exactly  like 
the  original  vibrations  produced  by  the  voice  of  the  speaker. 
These  vibrations  of  the  second  diaphragm  send  out  new  air 
waves  that  are  very  faithful  counterparts  of  the  original  air 
waves  that  fell  upon  the  first  diaphragm.  The  two  sets  of 
air  waves  being  alike,  the  resulting  sensations  produced  in 
the  hearers  are  alike.  Not  only  different  words  but  also 
different  voices  may  be  recognized.  The  arrangement 
being  the  same  at  both  stations,  the  apparatus  works  in 
either  direction.  (See  Appendix  M.) 

(a.)  The  reproduced  sound  is  somewhat  feeble  but  remarkably- 
clear  and  distinct.  The  second  telephone  should  be  held  close  to 
the  ear  of  the  listener.  Sometimes  there  are,  in  the  same  circuit, 
two  or  more  instruments  at  each  station,  so  that  each  operator  may 
hold  one  to  the  ear  and  the  other  to  the  mouth  ;  or  the  listener  may 
place  one  at  each  ear.  When  the  stations  are  a  considerable  dis- 
tance apart,  one  binding  post  of  each  instrument  may  be  connected 
with  the  earth,  as  in  the  case  of  the  telegraph  (§  395). 

(&.)  It  is  to  be  distinctly  noticed  that  the  sound  waves  are  not 
transmitted  from  one  station  to  the  other.  "The  airwaves  are 
spent  in  producing  mechanical  vibrations  of  the  metal ;  these  create 
magnetic  disturbances  which  excite  electrical  action  in  the  wire, 
and  this  again  gives  rise  to  magnetic  changes  that  are  still  further 
converted  into  the  tremors  of  the  distant  diaphragm,  and  these 
finally  reappear  as  new  trains  of  air  waves  that  affect  the  listener." 

447.  The  Phonograph.— This  is  an  instrument 
for  recording  sounds  and  reproducing  them  after  any 
length  of  time.  (See  Appendix  N.) 

(a.)  The  receiving  apparatus  consists  of  a  mouth-piece  and 
vibrating  disc  like  those  of  the  telephone.  At  the  back  of  the 
disc  is  a  short  needle  or  style  for  recording  the  vibrations  upon  a 
sheet  of  tinfoil  moving  under  it.  This  tinfoil  is  placed  upon  a  metal 


288  COMPOSITION  OF  SOUND   WAVES. 

cylinder  about  a  foot  (30  cm.}  long.  The  cylinder  has  a  spiral 
groove  upon  its  curved  surface  and  a  similar  thread  upon  its  axis, 
which  turns  in  a  fixed  nut.  As  the  cylinder  is  turned  by  a  crank, 
the  threads  upon  the  axis  give  the  cylinder  a  lengthwise  motion. 
The  style  is  placed  in  position  over  one  of  the  tinfoil  covered 
grooves  of  the  cylinder.  As  the  cylinder  revolves,  a  projection  in 
front  of  the  style  crowds  the  foil  down  into  the  groove.  The  needle 
follows  in  the  channel  thus  made,  and,  as  it  vibrates,  records  a  suc- 
cession of  dots  in  the  tinfoil.  These  dots  constitute  the  record.  To 
the  naked  eye  they  look  alike,  but  the  microscope  reveals  differences 
corresponding  to  pitch,  loudness,  and  timbre. 

(&.)  To  reproduce  the  sound,  the  style  is  lifted  from  the  foil,  the 
cylinder  turned  back  to  its  starting-point,  the  style  placed  in  the 
beginning  of  the  groove,  and  the  crank  turned.  The  style  passes 
through  the  channel  and  drops  into  the  first  yidentation  ;  the  disc 
follows  it.  The  style  rises  and  drops  into  each  of  the  succeeding 
indentations,  the  disc  following  its  every  motion  with  a  vibration. 
The  original  vibrations  made  the  dots ;  the  dots  are  now  making  simi- 
lar vibrations.  Sound  waves  made  the  original  vibrations  ;  now  the 
reproduced  vibrations  create  similar  sound  waves.  The  reproduced 
sounds  are  a  little  muffled  but  not  indistinct,  each  of  the  three 
qualities  (§  430)  being  recognizable.  The  principle  may  be  applied 
to  any  implement  or  toy  that  makes  a  sound  as  well  as  to  the  voice. 
Perfectly  simple ;  equally  wonderful. 

448.  Coincident  Waves, — In  the  case  of  water 
waves,  when  crest  coincides  with  crest  the  water  reaches  a 
double  height.     So  with  sound  waves,  when  condensation 
coincides  with  condensation,  this  part  of  the  wave  will  be 
more  condensed ;  when  rarefaction  coincides  with  rarefac- 
tion, this  part  of  the  wave  will  be  more  rarefied.     This 
increased  difference  of  density  in  the  two  parts  of  the  wave 
means  increased  loudness  of  the  sound,  because  there  is  an 
increased  amplitude  of  vibration  for  the  particles  consti- 
tuting the  wave. 

449.  Reinforcement  of  Sound.— This  increased 
intensity  may  result  from  the  blending  of  two  or  more 
series  of  similar  waves  in  like  phases,  or  from  the  union  of 


COMPOSITION  OF  SOUND    WAVES. 


289 


direct  and  reflected  waves  in  like  phases.  Under  such 
circumstances,  one  set  of  waves  is  said  to  reinforce  the 
other.  The  phenomenon  is  spoken  of  as  the  reinforce- 
ment of  sound. 

45O.  Resonance. — Resonance  is  a  variety  of  the 
reinforcement  of  sound  due  to  sympathetic  vibrations. 
'The  resonant  effects  of  solids  were  shown  in  §  444. 
The  resonance  of  an  air  column  is  well  shown  by  the 
following  experiments: 

(a.)  When  a  sounding  tuning-fork  is  held  over  the  mouth  of  a 
glass  jar,  18  or  20  inches 
deep,  a  feeble  sound  is 
heard.  By  carefully  pour- 
ing in  water,  we  notice 
that  when  the  liquid 
reaches  a  certain  level, 
the  sound  suddenly  be- 
comes much  louder.  The 
water  has  shortened  the 
air  column  until  it  is  able 
to  vibrate  in  unison  with 
the  fork.  If  more  water 
be  now  poured  in,  the  in- 
tensity of  the  sound  is 
lessened.  If  a  fork  of  dif- 
ferent vibration  be  used, 
the  column  of  air  that 
gives  the  maximum  reso- 
nance will  vary,  the  air 
column  becoming  shorter 
as  the  rate  of  vibration  of 
the  fork  increases.  The 
length  of  the  air  column 
is  one-fourth  the  length  of  the  wave  produced  by  the  fork. 


FIG.  226. 


Why? 


(6.)  Fig.  227  represents  Savart's  bell  and  resonator.     The  bell, 

on  being  rubbed  with  the  bow,  produces  a  loud  tone.    The  resonator 

is  a  tube  with  a  movable  bottom.     The  length  of  the  resonant  air 

column  is  changed  by  means  of  this  movable  bottom.    The  point 

13 


290 


COMPOSITION  OF  SOUND    WAVES. 


at  which  the  reinforcement  of  sound  is  greatest  is  easily  found  by 

trial.  If,  when  the  sound 
of  the  bell  has  become 
hardly  audible,  the  tube  be 
brought  near,  the  resonant 
effect  is  very  marked. 

451.  Interference 
of  Sound. — If,  while 
a  tuning-fork^is  vibrat- 
ing, a  second  fork  be  set 

in  vibration,  the  waves  from  the  second  must  traverse  the 
air  set  in  motion  by  the  former.  If  the  waves  from  the  two 
forks  be  of  equal  length,  as  will  be  the  case  when  the  two 


FIG.  228. 

forks  have  the  same  pitch,  and  the  forks  be  any  number  of 
whole  wave  lengths  apart,  the  two  sets  of  waves  will  unite 
in  like  phases  (Fig.  228),  (condensation  with  condensation, 


FIG.  229. 

etc.),  and  a  reinforcement  of  sound  will  ensue.  But  if  the 
second  fork  be  placed  an  odd  number  of  half  wave  lengths 
behind  the  other,  the  two  series  of  waves  will  meet  in 
opposite  phases ;  where  the  first  fork  requires  a  condensa- 
tion, the  second  will  require  a  rarefaction.  The  two  sets 


COMPOSITION  OF  SOUND    WAVES.  291 

of  waves  will  interfere,  the  one  with  the  other.  If  the 
waves  be  of  equal  intensity,  the  algebraic  s»m  of  these 
component  forces  will  be  zero.  The  air  particles,  thus 
acted  upon,  will  remain  at  rest ;  this  means  silence.  In 
Fig.  229,  an  attempt  is  made  to  represent  this  effect  to  the 
eye,  the  uniformity  of  tint  indicating  the  absence  of  con- 
densations and  rarefactions.  Tfius,  by  adding  sound 
to  sound,  both  may  be  destroyed.  This  is  the  lead- 
ing characteristic  property  of  wave  motion.  The 
phenomenon  here  described  is  called  interference 
of  sound. 


(a.)  The  sound  of  a  vibrating  tuning-fork  held  in  the  hand  is 
almost  inaudible.  The  feebleness  results  largely  from  interference. 
As  the  prongs  always  vibrate  in  opposite  directions  at  the  same 
time,  one  demands  a  rarefaction  where  the  other  demands  a  con- 
densation. By  covering  one  vibrating  prong  with  a  pasteboard 
tube  the  sound  is  more  easily  heard.  (Fig.  230.) 

(&.)  Hold  a  vibrating  tuning-fork  near  the  ear,  and  slowly  turn 
it  between  the  fingers.  During  a  single  complete  rotation,  four 


292  COMPOSITION  OF  SOUND 


positions  of  full  sound  and  four  positions  of  perfect  silence  will  be 
found.  When  a  side  of  the  fork  is  parallel  to  the  ear,  the  sound 
is  plainly  audible  ;  when  a  corner  of  a  prong  is  turned  toward  the 
ear,  the  waves  from  one  prong  completely  destroy  the  waves  started 
by  the  other.  The  interference  is  complete. 

(c.)  Over  a  resonant  jar,  as  shown  in  Fig.  226,  slowly  turn  a 
vibrating  tuning-fork.  In  four  positions  of  the  fork  we  have  loud, 
resonant  tones  ;  in  four  other  positions  we  have  complete  inter- 
ference. If,  while  the  fork  is  in  one  of  these  positions  of  inter- 
ference, a  pasteboard  tube  be  placed  around  one  of  the  vibrating 
prongs,  a  resonant  tone  is  instantly  heard  ;  the  cause  of  the  inter- 
ference has  been  removed. 

4:52.  Beats.  —  If  two  tuning-forks,  A  and  B,  vibrating 
respectively  255  and  256  times  a  second,  be  set  in  vibration 
at  the  same  time,  their  first  waves  will  meet  in  like  phases 
and  the  result  will  be  an  intensity  of  sound  greater  than 
that  of  either.  After  half  a  second,  B  having  gained  half 
a  vibration  upon  J,  the  waves  will  meet  in  opposite  phases 
and  the  sound  will  be  weakened  or  destroyed.  At  the  end 
of  the  second  we  shall  have  another  reinforcement  ;  at  the 
middle  of  the  next  second  another  interference.  This 
peculiar  palpitating  effect  is  due  to  a  succession 
of  reinforcements  and  interferences,  and  is  called 
a  beat.  The  number  of  beats  per  second  equals  the  dif- 
ference of  the  two  numbers  of  vibrations. 

(a.)  In  a  quiet  room,  strike  simultaneously  one  of  the  lower  white 
keys  of  a  piano  and  the  adjoining  black  key.  The  beats  will  be 
heard. 

(6.)  If  the  two  tuning-forks  described  in  §  443,  one  being  loaded 
as  there  mentioned,  be  simultaneously  sounded,  the  beats  will  be 
very  perceptible.  Replacing  the  3-cent  piece  success]  vely  by  a  silver 
half-dime  and  a  dime,  the  number  of  beats  will  be  successively 
increased. 

(c.)  If  two  large  organ  pipes,  having  exactly  the  same  tone,  be 
simultaneously  sounded,  a  low,  loud,  uniform  sound  will  be  pro- 
duced. If  an  aperture  be  made  in  the  upper  part  of  one  of  the 
walls  of  one  of  the  pipes  and  closed  by  a  movable  plate,  the  tone 


COMPOSITION  OF  SOUND    WAVES.  293 

produced  by  the  pipe  may  be  changed  at  will.  The  more  the 
aperture  is  opened,  the  higher  the  pitch.  In  this  manner,  slightly 
raise  the  pitch  of  one  of  the  pipes.  If  the  pipes  be  sounded  in 
succession,  even  a  trained  ear  would  probably  fail  to  detect  any 
difference.  If  they  be  sounded  simultaneously,  the  sound  will  be 
of  varying  loudness,  very  marked  jerks  or  palpitations  being  per 
ceptible. 

453.  Practical  Effect  of  Beats.— The  human 
car  may  recognize  about  38;000  different  sounds.      If  a 
string,  for  example,  vibrating  400  times  per  second  were 
sounded,  and  one  vibrating  401  times  per  second  were 
subsequently  sounded,  the  ear  would  probably  fail  to  detect 
any  difference  between  them.    But  if  they  were  sounded 
simultaneously,  the  presence  of  one  beat  each  second  would 
clearly  indicate  the  difference.     Unaided  by  the  beats,  the 
ear  can  detect  about  one  per  cent,  of  the  38,000  sounds 
lying  within  the  range  of  the  human   ear.    Beats  are, 
therefore,  very  important  to  the  tuner  of  musical  instru* 
ments.     To  bring  two  slightly  different  tones  into  unison, 
he  has  only  to  tune  them  so  that  the  beats  cease. 

454.  Vibrations  of  Strings.— The  laws  of  musical  tones 
are  most  conveniently  studied  by  means  of  stringed  instruments. 
In  the  violin,  etc.,  the  strings  are  set  in  vibration  by  bowing  them. 
The  hairs  of  the  bow,  being  rubbed  with  rosin,  adhere  to  the  string 
and  draw  it  aside  until  slipping  takes  place.     In  springing  back, 
the  string  is  quickly  caught  again  by  the  bow  and  the  same  action 
repeated.     In  the  harp  and  guitar,  the  strings  are  plucked  with  the 
finger.     In  the  piano,  the  wires  are  struck  by  little  leather-faced 
hammers  worked  by  the  keys.     The  vibrations  of  the  string,  and 
consequently  the  pitch,  depend  upon  the  string  itself.     The  manner 
of  producing  the  vibrations  has  no  effect  upon  the  pitch. 

455.  Laws  of  the  Vibrations  of  Strings.— 

The  following  are  important  laws  of  musical  strings : 

(1.)  Other  conditions  being  the  same,  the  number  of 
vibrations  per  second  varies  inversely  as  the  length  of  the 
string. 


294:  COMPOSITION  OF  SOUND   WAVES. 

(2.)  Other  conditions  being  the  same,  the  number  of 
vibrations  per  second  varies  directly  as  the  square  root  of 
the  stretching  weight,  or  tension. 

(3.)  Other  conditions  being  the  same,  the  number  of 
vibrations  per  second  varies  inversely  as  the  square  root  of 
the  weight  of  the  string  per  linear  unit. 

(<z.)  All  of  these  laws  may  be  roughly  illustrated  by  means  of  a 
violin.  The  length  of  the  string  may  be  altered  by  fingering  ;  the 
tension  may  be  changed  by  means  of  the  screws  or  keys ;  the  effects 
of  the  third  law  may  be  shown  by  the  aid  of  the  four  strings. 

(&.)  For  the  illustration  of  these  laws  the  sonometer,  shown  in 
Fig.  231,  is  generally  used.  The  length  of  the  string  is  determined 


FIG.  231. 

by  the  two  fixed  bridges,  or  by  one  of  them  and  the  movable  bridge 
which  may  be  employed  for  changing  the  length  of  the  vibrating 
part  of  the  string  ;  the  tension  is  regulated  by  weights,  which  may 
be  changed  at  pleasure ;  the  third  law  may  be  verified  by  using 
different  strings  of  known  weights.  Iron  and  platinum  wires  of 
the  same  diameters  are  frequently  used  for  this  purpose. 

(c.)  From  these  laws  it  follows,  for  example,  that  a  string  of  half 
the  length,  or  four  times  the  tension,  or  one-fourth  the  weight  of  a 
given  string  will  vibrate  just  twice  as  fast  as  the  given  string,  i.e., 
twice  as  fast  on  account  of  any  one  of  these  three  variations.  A 
string  of  one-third  the  length,  or  nine  times  the  tension,  or  one- 
ninth  the  weight  of  a  given  string,  will  vibrate  three  times  as  fast 
as  the  given  string  ;  and  so  on. 

456.    The    Musical    Scale.— Starting  from    any 


COMPOSITION  OF  SOUND    WAVES.  295 

arbitrary  tone  or  absolute  pitch,  the  voice  rises  or  falls  in 
a  manner  very  pleasing  to  the  ear,  by  eight  steps  or  inter- 
vals. The  whole  series  of  musical  tones  may  be  divided 
into  octaves,  or  groups  of  eight  tones  each,  the  relation 
between  any  two  members  of  one  group  being  the  same  as 
the  relation  between  the  corresponding  members  of  any 
other  group.  The  eighth  of  the  first  group  becomes  the 
first  of  the  second.  The  intervals  between  the  successive 
tones  are  not  precisely  the  same,  as  will  be  seen  from  the 
next  paragraph. 

457.   Relative  Numbers  of  Vibrations.— A 

string  vibrating  half  as  rapidly  as  a  given  string,  will  give 
its  octave  below ;  one  vibrating  twice  as  rapidly,  its  octave 
above.  The  ratio  of  the  number  of  vibrations  correspond- 
ing to  the  interval  of  an  octave  is,  therefore,  1:2.  The 
relative  number  of  vibrations  corresponding  to  the  tones 
which  constitute  the  major  diatonic  scale  (gamut)  are  as 
follows : 


Relative  Names,         -      :,  ^,    1,  2,     3,  4,  5,  6,  7,  8. 

Absolute  Names,    -          -        -    C,  D,    E,  F,  G,  A,  B,  C. 

Syllables,    -                           -do,  re,    mi,  fa,  sol,  la,  si,  do. 

Relative  Numbers  of  Vibrations,  I,  f,     £,  f,  f,  f,  -1/,  2. 

24,  27,   30,  32,  36,  40,  45,  48. 

458.    Absolute   Numbers   of  Vibrations. — 

Knowing  the  number  of  vibrations  which  constitute  the 
tone  called  do,  the  absolute  number  of  vibrations  of  any 
of  the  other  tones  of  the  scale  may  be  obtained  by  multi- 
plying the  number  of  vibrations  of  do  by  the  ratio  between 
it  and  that  of  the  given  tone  as  shown  above.  Thus,  if  C 
have  256  vibrations  per  second,  G  will  have  256  x  f  —  384 


296  COMPOSITION  OF  SOUND    WAVES. 

vibrations  per  second;  its  octave  will  have  512;  the  fifth 
of  its  octave  will  have  512  x  f  =  768.  If  F  be  given  352 
vibrations,  G  will  have  352  -i-  f  =  264.  Thus,  knowing  (7, 
any  given  tone  may  have  its  number  of  vibrations  deter- 
mined by  multiplying  by  the  proper  ratio. 

459.  Absolute  Pitch. — The  number  of  vibrations 
constituting  the  tone  called  C  is  purely  arbitrary.     The 
assignment  of  256  complete  vibrations  to  middle  C  is  com- 
mon, but  the  practice  of  musicians  is  not  uniform.    A 
certain  tuning-fork  deposited  in  the  Conservatory  of  Music 
at  Paris  is  the  standard  for  France;  it  assigns  261  vibra- 
tions per  second  to  middle  C.     The  standard  tuning-fork 
adopted  by  English  musicians  and  deposited  with   the 
Society  of  Arts  in  London,  gives  264  vibrations  to  middle 
C.    Multiplying  the  numbers  in  the  last  line  of  §  457  by 
11,  we  shall  have  the  absolute  numbers  of  vibration  for 
the  several  tones  of  the  gamut  corresponding  to  this 
standard. 

(a.)  Whatever  be  the  standard  thus  adopted,  an  instrument  will 
be  in  tune  when  the  relative  number  of  vibrations  is  correct.  The 
string  that  produces  the  tone  G  must  always  vibrate  three  times 
while  the  one  producing  C  vibrates  twice,  or  36  times,  while  the 
latter  vibrates  24  times.  While  the  string  yielding  D  vibrates  27 
times,  the  string  yielding  B  must  vibrate  45  times  ;  and  so  on. 

(&.)  Middle  C  is  the  tone  sounded  by  the  key  of  a  piano  at  the  left 
of  the  two  black  keys  near  the  middle  of  the  key-board.  It  is 
designated  by  C\.  Its  octaves  below  and  above  are  designated  as 
follows : 

cu,  a.,,  <?,  a,  c»  a,  c4. 

460.  Fundamental  Tones  and  Overtones. — 

A  string  may  vibrate  transversely  as  a  whole,  or  as  inde- 
pendent segments.  Such  segments  will  be  aliquot  parts 
of  the  whole  string,  and  separated  from  each  other  by  points 


COMPOSITION  OF  SOUND    WAVES.  297 

of  no  motion,  called  nodes  or  nodal  points.  The  tone 
produced  by  the  vibrations  of  the  whole  length  of 
a  string  is  called  its  fundamental  tone.  Tlie  tones 
produced  by  the  vibrations  of  the  segments  of  a 
string  are  called  its  overtones  or  harmonics. 

(a.)  The  fact  that  a  string  may  thus  vibrate  in  segments,  with  the 
further  fact  that  a  string,  or  other  sounding  body,  can  hardly  be  made 
to  vibrate  as  a  whole  without  vibrating  in  segments  at  the  same  time, 
furnishes  a  means  of  explaining  quality  or  timbre  of  sound.  (§  430.) 

461.  Fundamental    Tones.— When    a    string 
vibrates  so  as  to  produce  its  fundamental  tone,  its  extreme 
positions  may  be  represented   ^~~—— — ^^ 

by  the  continuous  and  the 

J  FIG.  232. 

dotted  lines  of   Fig.   232. 

This  effect  is  obtained  by  leaving  the  string  free  and  bowing 
it  near  one  of  its  ends.  If  a  number  of  little  strips  of 
paper,  doubled  in  the  middle,  be  placed  like  riders  upon 
the  string,  and  the  string  bowed  as  just  described,  all  of 
the  riders  will  be  thrown  up  and  most  of  them  off.  This 
shows  that  the  whole  string  vibrates  as  one  string ;  that 
there  is  no  part  of  it  between  the  fixed  ends  that  is  not  in 
vibration. 

462.  The  First  Overtone.— If  the  string  of  the, 
sonometer  be  touched  exactly  at  its  middle  with  a  finger, 
or  better,  with  a  feather,  a  higher  tone  is  produced  when 
the  string  is  bowed.     This  higher  tone  is  the  octave  of  the 
fundamental.     The  string  now  vibrates  in  such  a  way  that 
the  point  touched  remains  at  rest.    Its  extreme  positions 

C  N  D  may  be  represented  by  the 

of   Fiff.   233.      The 


point  N  is  acted  upon  by 
two  equal  and  opposite  forces ;   it  is  urged  to  move  both 


298  COMPOSITION  OF  SOUND    WAVES. 

ways  at  the  same  time,  and,  consequently,  does  not  move 
at  all,  but  remains  at  rest  as  a  node.  The  tone  is  due  to 
the  vibrations  of  the  two  halves  of  the  string,  which  thus 
give  the  octave  instead  of  the  fundamental.  The  existence 
of  the  node  and  segments  will  continue  for  some  time  after 
the  finger  is  removed.  If  riders  be  placed  at  (7,  N  and  D, 
the  one  at  N  will  remain  at  rest  while  those  at  C  and  D 
^will  probably  be  dismounted. 

463.  Higher  Overtones.— In  like  manner,  if  the 
vibrating  string  be  touched  at  exactly  one-third,  one-fourth 


FIG.  234. 


or  one-fifth  of  its  length  from  one  end,  it  will  divide  into 
three,  four  or  five  segments,  with  vibrations  three,  four  or 
five  times  as  rapid  as  the  fundamental  vibrations.  If 
touched  at  one-third  its  length,  as  represented  in  Fig.  234, 
the  tone  will  be  the  fifth  to  the  octave  of  the  fundamental ; 


COMPOSITION  OF  SOUND    WAVES.  299 

if  touched  at  one-fourth  its  length,  the  tone  will  be  the 
second  octave  above.  Of  course,  any  other  aliquot  part  of 
the  length  of  the  string  may  be  used.  In  any  case,  the 
experiment  with  riders  may  be  repeated  to  indicate  the 
position  of  the  segments  and  nodes. 

464.  Quality  or  Timbre.—  As  a  sounding  body 
vibrates  as  a  whole  and  in  segments  at  the  same  time,  the 
fundamental  and  the  harmonics  blend.  The  resultant 
effect  of  this  blending  of  fundamentals  and  harmonics  con- 
stitutes what  we  call  the  quality  or  timbre  of  the  sound. 
We  recognize  the  voice  of  a  friend  not  by  its  loudness  nor 
by  its  pitch,  but  by  its  quality.  When  a  piano  and  violin 
sound  the  same  tone,  we  easily  distinguish  the  sound  of 
one  from  that  of  the  other,  because,  while  the  fundamentals 
are  alike,  the  harmonics  are  different.  Hence,  the  total 
effects  of  the  fundamentals  and  the  harmonics,  or  the 
qualities,  are  different.  The  possible  combinations  of  fun- 
damentals and  harmonics,  or  forms  of  vibratory  motion, 
are  innumerable. 


.—  The  pupil  is  advised  to  read  the  section  on  Harmonics  in 
the  third  of  Tyndall's  Lectures  On  Sound,  Chap.  Ill,  §  9.  Become 
the  owner  of  the  book,  if  you  can. 

465.  Classes  of  Musical  Instruments.  —  Mu- 

sical instruments  may  be  divided  into  two  classes,  stringed 
instruments  and  wind  instruments.  The  sounds  sent  forth 
by  stringed  instruments  are  due  to  the  regular  vibrations  of 
solids  ;  those  sent  forth  by  wind  instruments,  to  the  regular 
vibrations  of  columns  of  air  confined  in  sonorous  tubes. 

466.  Sonorous  T  vibes.  —  The  material  of  which  a 
sonorous  tube  is  made  does  not  affect  the  pitch  or  loud- 
ness  of  the  sound,  but  does  determine  its  timbre  or  quality. 


300 


COMPOSITION  OF  SOUND    WAVES. 


Sonorous  tubes  are  called  mouth  pipes  or  reed  pipes, 
according  to  the  way  in  which  the  column  of  air  is  made 
to  vibrate. 

467.  Stopped  Pipes.— A  sonorous  tube  may  have 
one  end  stopped  or  both  ends  open.  In  either  case,  the 
tones  are  due  to  waves  of  condensation  and  rarefaction 
transmitted  through  the  length  of  the  tube.  In  a  stopped 
pipe,  the  air  particles  at  the  closed  end  have  no  oppor- 
tunity for  vibration ;  this  end  of  the  tube  is,  therefore,  a 
node.  The  mouth  of  the  tube  affords  opportunity  for  the 
greatest  amplitude.  The  length  of  such  a  pipe  is  one- 
fourth  the  wave  length  of  its  fundamental  tone. 

468.  Open  Pipes. — In  an  open 
pipe,  the  ends  afford  opportunity  for 
the  greatest    amplitude;     the    node 
will  fall  at  the  middle.    The  air  col- 
umn will  now  equal  one-half  the  wave 
length;    the   tone  will  be  an  octave 
higher   than    that    produced   by    a 
stopped  pipe  of  the  same  length. 

469.  Organ  Pipes. — The  organ 
pipe  affords  the  best  illustration   of 
mouth  pipes.     Fig.  235  represents  the 
most  common  kind  of  organ  pipe, 
which  may  be  of  wood  or  metal,  rect- 
angular or  cylindrical.     The  air  cur- 
rent from  the  bellows  enters  through  P, 
passes  into  a  small  chamber,  emerges 
through  the  narrow  slit  i,  and  escapes 
in  puffs  between  a  and  #,  the  two  lips 


COMPOSITION  OF  SOUND    WAVES.  301 

of  the  mouth.  The  puffs  are  due  to  the  fact  that  the  air 
current  from  i  strikes  upon  the  bevelled  lip  a  and  breaks 
into  a  flutter.  The  puffing  sound  thus  produced  consists 
of  a  confused  mixture  of  many  faint  sounds.  The  air 
column  of  the  pipe  can  resound  to  only  one  of  these  tones. 
The  resonance  of  the  air  column  brought  about  in  this 
way  constitutes  the  tone  of  the  pipe. 

(a.)  We  see,  from  the  above,  that  it  makes  little  difference  how 
the  pulses  of  air  are  produced.  A  vibrating  tuning-fork  held  at 
the  mouth  of  a  pipe  of  the  same  pitch  is  enough  to  make  the  pipe 
sound  forth  its  tone.  The  production  of  the  tone  is  strictly  analo- 
gous to  the  phenomena  mentioned  in  §  450. 

47O.  Reed  Pipes.— A  simple  reed  pipe  may  be 
made  by  cutting  a  piece  of  wheat  straw  eight  inches 
(20  cm.}  long  so  as  to  have  a  knot  at  one  end.  At  r, 
about  an  inch  from  the  knot,  cut  inward  about  a  quarter  of 
the  straw's  diameter ;  turn  the  knife-blade  flat  and  draw  it 
toward  the  knot.  The  strip  rr'  thus  raised  is  a  reed  ;  the 
straw  itself  is  a  reed  pipe.  When  the  reed  is  placed  in  the 
mouth,  the  lips  firmly  closed  around  the  straw  between 


FIG.  236. 

r  and  s  and  the  breath  driven  through  the  apparatus,  the 
reed  vibrates  and  thus  produces  vibrations  in  the  air  col- 
umn of  the  wheaten  pipe.  Notice  the  pitch  of  the  musical 
sound  thus  produced.  Cut  off  two  inches  from  the  end 
of  the  pipe  at  s.  Blow  through  the  pipe  as  before  and 
notice  that  the  pitch  is  raised.  Cut  off,  now,  two  inches 
more,  and  upon  sounding  the  pipe  the  pitch  will  be  found 
to  be  still  higher.  We  thus  see  that  the  pipe  and  not  the 
reed  determines  the  pitch.  In  each  of  these  three  cases 


302  COMPOSITION  OF  SOUND    WAVES. 

we  had  the  same  reed  which  was  obliged  to  adapt  itself  to 
the  different  vibrations  of  the  different  air  columns. 

(a.)  It  will  be  easily  seen  how  reeds  may  be  used  in  musical  in- 
struments. The  accordeon,  clarionet  and  vocal  apparatus  are  reed 
instruments. 

471.  Effect  of  Lateral  Openings*  —  Certain 
wind  instruments,  like  the  flute,  fife  and  clarionet,  have 
holes  in  the  sides  of  the  tube.  On  opening  one  of  these 
holes,  opportunity  is  given  for  greatest  amplitude  at  that 
point.  This  changes  the  distribution  of  nodes,  affects  the 
length  of  the  segments  of  the  vibrating  air  columns,  and 
thus  determines  the  wave  length  or  pitch  of  the  tone. 

EXERCISES. 

1.  If  a  musical  sound  be  due  to  144  vibrations,  to  how  many  vibra- 
tions will  its  3d,  5th,  and  octave,  respectively,  be  due  ? 

2.  Determine  the  length  of  a  tube  open  at  both  ends  that  can 
resound  the  tone  of  a  tuning-fork  vibrating  512  times  a  second. 

3.  A  certain  string  vibrates  100  times  a  second,    (a.)  Find  the 
number  of  vibrations  of  a  similar  string,  twice  as  long,  stretched 
by  the  same  weight.    (&.)  Of  one  half  as  long. 

4.  A  certain  string  vibrates  100  times  per  second.    Find  the  num- 
ber of  vibrations  of  another  string  that  is  twice  as  long,  and  weighs 
four  times  as  much  per  foot  and  is  stretched  by  the  same  weight. 

5.  A  musical  string  vibrates  200  times  a  second.     State  (a.)  what 
takes  place  when  the  string  is  lengthened  or  shortened  with  no 
change  of  tension,  and  (6.)  what  change  takes  place  when  the  ten- 
sion is  made  more  or  less,  the  length  remaining  the  same. 

6.  A  tube  open  at  both  ends  is  to  produce  a  tone  corresponding 
(«.)  to  32  vibrations  per  second.     Taking  the  velocity  of  sound  as 
1120  ft.,  find  the  length  of  the  tube.     (&.)  If  the  number  of  vibra- 
tions be  4480,  find  the  length  of  the  tube. 

7.  (a.)  Find  the  length  of  an  organ  pipe  whose  waves  are  four 
feet  long,  the  pipe  being  open  at  both  ends.     (&.)  Find  the  length, 
the  pipe  being  closed  at  one  end. 

8.  A  tuning-fork  produces  a  strong  resonance  when  held  over  a 
jar  15  inches  long,    (a.}  Find  the  wave  length  of  the  fork.    (6 )  Find 
the  wave  period. 


REVIEW.  303 

9.  If  two  tuning-forks  vibrating  respectively  256  and  259  times 
per  second  be  simultaneously  sounded  near  each  other,  what  phe- 
nomena would  follow  ? 

10.  A  musical  string,  known  to  vibrate  400  times  a  second,  gives 
a  certain  tone.     A  second  string  sounded  a  moment  later  seems  to 
give  the  same  tone.    When  sounded  together,  two  beats  per  second 
are  noticeable,    (a.)  Are  the  strings  in  unison?    (&.)  If  not,  what  is 
the  rate  of  vibration  of  the  second  string  ? 

11.  If  a  tone  be  produced  by  256  vibrations  per  second,  what  num- 
bers will  correspond  to  its  third,  fifth  and  octave  respectively  ? 

12.  If  a  tone  be  produced  by  264  vibrations  per  second,  what 
number  will  represent  the  vibrations  of  the  tone  a  fifth  above  its 
octave  ? 

Recapitulation. — In  this  section  we  have  considered 
Sympathetic  Vibrations  and  Sounding 
Boards ;  the  Telephone  and  Phonograph ; 
Reinforcement  and  Resonance ;  Interfer- 
ence and  Beats ;  Vibrations  of  Strings ;  the 
Musical  Scale ;  Absolute  Pitch ;  Funda- 
mental Tones ;  Overtones ;  the  Quality  of 
Sounds;  Musical  Instruments. 

KEVIEW  QUESTIONS  AND  EXERCISES. 

1.  (a.)  Define  sound  ;  (&.)  give  its  cause ;  (c.)  mode  of  propagation 
and  (d.)  velocity. 

2.  (a.)  Give  the  rate  at  which  sound  is  transmitted  in  air.     (6.) 
How  is  it  affected  by  temperature  ?    (c.)  Give  the  law  of  Reflection. 
(d.)  How  may  it  be  illustrated  ? 

3.  (a.)  What  is  capillary  attraction  ?    (&.)  Give  three  illustrations 
of  the  importance  of  capillary  action  in  the  operations  of  nature. 

4.  (a.)  Describe  an  experiment  showing  the  expansibility  of  the 
air.    (6.)  Give  the  laws  of  the  Pendulum. 

5.  (a.)  On  what  does  the  loudness  of  sound  depend?    (&.)  How 
may  the  pitch  of  strings  be  varied  ?    (c.)  Give  the  relative  number 
of  vibrations  in  the  major  diatonic  scale,  and  (d.)  find  the  number  of 
vibrations  for  A2. 

6.  (a.)  Represent  by  a  diagram,  a  lever  of  the  first  class,  in  which 
one  pound  will  balance  five.    (6.)  Give  the  laws  of  falling  bodies. 

7.  Explain  the  Artesian  well  by  a  diagram. 


304  REVIEW. 

8.  (a. )  What  will  be  the  momentum  of  a  ball  weighing  two  ounces 
after  falling  4|  seconds  ?    (&.)  A  stone  weighing  20  Ibs.  on  the  sur- 
face of  the  earth,  would  weigh  how  much  at  an  elevation  of  2000 
miles  from  the  surface  ? 

9.  Define  (a.)  wave  length  ;   (&.)  wave  period  ;    (c.)  amplitude  of 
vibration  ;  (d.)  phase  of  a  vibrating  particle. 

10.  (a.)  What  would  be  the  effect  of  making  a  small  hole  at  the 
highest  point  of  a  siphon  in  action  ?    (ft.)  What  effect  upon  the  action 
of  a  siphon  would  be  produced  by  carrying  it  up  a  mountain?    (c.) 
What  effect  would  follow  if  the  atmosphere  were  suddenly  to  be- 
come denser  than  the  liquid  being  moved  ? 

11.  Describe  (#.)  a  complete  soundwave  and  (&.)  its  manner  of 
propagation,     (c.)  How  does  the  transmission  of  sound  through  a 
smooth  tube  differ  from  its  transmission  through  the  open  air  ? 

12.  Give  the  laws  for  pressure  of  liquids  and  explain  each  by 
some  fact  or  experiment. 

13.  (a.)  Distinguish  clearly  between  noise  and  music.     (&.)  What 
is  meant  by  timbre  ?    (c.)  By  pitch  ? 

14.  (a.)  Give  three  examples  of  musical  sounds  that  agree  in  one 
and  differ  in  two  elements  or  characteristics,  making  a  different 
element  agree  each  time. 

15.  Give  three  examples  of  musical  sounds  that  differ  in  one  and 
agree  in  two  elements,  making  a  different  element  differ  each  time. 

16.  (a.)  What  are  sympathetic  vibrations  ?    (6.)  How  may  they  be 
produced  ?    (c.)  What  are  beats  ?    (d.}  How  may  they  be  produced? 

17.  (a.)  What  is  Archimedes'  Principle  ?    (&.)  How  is  it  applied  in 
finding  the  specific  gravity  of  a  solid  ? 

18.  How  much  water  per  hour  will  be  delivered  from  an  orifice  of 
2  inches  area  49  feet  below  the  surface  of  a  tank  kept  full  ? 

19.  Describe  the  telephone. 

20.  («.)  Describe  the  electrophorus.    (6.)  Explain  its  action. 

21.  (a.)  Describe  an  organ  pipe,    (b.)  Make  a  reed  pipe. 

22.  (a.}  Explain  the  charging  of  the  Leyden  jar  ;  (6.)  when  charged 
what  is  the  electric  condition  of  the  outside  and  inside  of  the  jar  ? 

23.  (a.)  A  body  falls  for  six  seconds ;  find  the  distance  traversed 
in  the  last  two  seconds  of  its  fall.    (6.)  How  far  will  a  body  fall  in 
•fa  of  a  second  beginning  at  the  end  of  four  seconds  ?    (c.)  Explain 
the  ''kick  "of  a  gun. 

24.  (a.)  Show  that  if,  in  an  Attwood's  machine,  one  weight  be  f 
as  heavy  as  the  other,  its  increment  of  velocity  will  be  £  that  of  a 
freely  falling  body.     (6.)  That  if  the  lighter  weight  be  f  of  the 
heavier,  its  increment  of  velocity  will  be  £  g. 


HEAT. 


ECTfON  I. 


TEMPERATURE,  THERMOMETERS,    EXPANSION. 

472.  Introductory  Quotation.—"  There  are  other  forces 
besides  gravity,  and  one  of  the  most  active  of  these  is  chemical  affin- 
ity.    Thus,  for  instance,  an  atom  of  oxygen  has  a  very  strong  attrac- 
tion for  one  of  carbon,  and  we  may  compare  these  two  atoms  to  the 
earth  and  a  stone  lodged  upon  the  top  of  a  house.     Within  certain 
limits,  this  attraction  is  intensly  powerful,  so  that  when  an  atom  of 
carbon  and  one  of  oxygen  have  been  separated  from  each  other,  we 
have  a  species  of  energy  of  position  just  as  truly  as  when  a  stone 
has  been  separated  from  the  earth.     Thus  by  having  a  large  quan- 
tity of  oxygen  and  a  large  quantity  of  carbon  in  separate  states,  we 
are  in  possession  of  a  large  store  of  energy  of  position.    When  we 
allowed  the  stone  and  the  earth  to  rush  together,  the  energy  of 
position  was  transformed  into  that  of  actual  motion  (§  159),  and  we 
should  therefore  expect  something  similar  to  happen  when  the 
separated  carbon  and  oxygen  are  allowed  to  rush  together.    This 
takes  place  when  we  burn  coal  in  our  fires,  and  the  primary  result, 
as  far  as  energy  is  concerned,  is  the  production  of  a  large  amount  of 
heat.    We  are,  therefore",  led  to  conjecture  that  heat  may  denote  a 
motion  of  particles  on  the  small  scale  just  as  the  rushing  together  of 
the  stone  and  the  earth  denotes  a  motion  on  the  large.     It  thus 
appears  that  we  may  have  invisible  molecular  energy  as  well  as 
visible  mechanical  energy" — Bcdfour  Stewart. 

473.  What    is   Heat  t—Heat  is  a  form  of  en- 
ergy.   It  consists  of  vibratory  motions  of  the  mole- 
cules of  matter  or  results  from  such  motions,  and 


306  TEMPERATURE. 

gives  rise  to  the  well  known  sensations  of  warmth 
and  cold.  By  means  of  these  effects  upon  the  animal 
body  it  is  generally  recognized.  Being  a  form  of  energy, 
it  is  a  measurable  quantity  but  not  a  material  substance. 

474.  What  is   Temperature  t—The  tempera- 
ture of  a  body  is  Us  state  considered  with  refer- 
ence to  its  ability  to  communicate  heat  to  other 
bodies.    It  is  a  term  used  to  indicate  how  hot  or  cold 
a  body  is.     When  a  body  receives  heat  its  temperature 
generally  rises,   but  sometimes   a    change    of   condition 
(§  53)  results  instead.    When  a  body  gives  up  heat,  its 
temperature  falls  or  its  physical  condition  changes. 

475.  An  Unsafe  Standard.— When  we  put  a  very  warm 
hand  into  water  at  the  ordinary  temperature,  we  say  that  the  water 
is  cold.    If  another  person  should  put  a  very  cold  hand  into  the 
same  water  he  would  say  that  the  water  is  warm.     If  a  person  place 
one  hand  in  water  freezing  cold  and  the  other  hand  in  water  as  hot 
as  he  can  endure,  and,  after  holding  them  there  some  time,  plunge 
them  simultaneously  into  water  at  the  ordinary  temperature,  the 
hand  from  the  cold  water  feels  warm  while  the  hand  from  the  hot 
water  feels  cold.     These  experiments  show  that  bodily  sensations 
cannot  be  trusted  to  measure  this  form  of  energy  that  we  call  heat. 

476.  Thermometers.  —  An    instrument    for 
measuring  temperature  is  called  a  thermometer. 
The  mercury  thermometer  is  the  most  common.     Its  ac- 
tion depends  upon  the  facts  that  heat  expands  mercury 
more  than  it  does  glass,  and  that  when  two  bodies  of  dif- 
ferent temperatures  are  brought  into  contact,  the  warmer 
one  will  give  heat  to  the  colder  one  until  they  have  a  com- 
mon temperature. 

477.  Graduation  of  Thermometers. — Ther- 
mometers are  graduated  in  different  ways,  but  in  all  cases 
there  are  two  fixed  points,  viz.,  the  freezing  and  the  boiling 


TEMPERA  TURE. 


307 


points  of  water ;  or,  more  accurately,  the  temperature  of 
melting  ice  and  the  temper- 
ature of  steam  as  it  escapes 
from  water  boiling  under 
a  pressure  of  one  atmos- 
phere. 

478.      Determination 
of  the  Freezing  Point.— 

Ice  in  contact  with  water  cannot 
be  raised  above  a  certain  tem- 
perature ;  water  in  contact  with 
ice  cannot  be  reduced  below  the 
same  temperature.  Here,  then, 
is  a  temperature  fixed  and  easily 
produced.  The  thermometer  is 
placed  in  melting  ice  or  snow 
contained  in  a  perforated  vessel. 


FIG.  237. 


When  the  mercury  column  has  come  to  rest,  a  mark  is  made  on  the 
glass  tube  at  the  level  of  the  mercury.  This  point  is,  for  the  sake 
of  brevity,  called  the  freezing  point. 

479.   Determination    of  the   Boiling    Point.— The 

temperature  of  steam  issuing  from  water  boiling  under  any  given 
pressure  is  invariable.  Fig.  238  represents  a  metal  vessel  in  which 
water  is  made  to  boil  briskly.  The  thermom- 
eter being  supported  as  represented  is  sur- 
rounded by  the  steam  but  does  not  touch  the 
water.  That  the  steam  may  not  cool  before 
it  comes  into  contact  with  the  thermometer, 
the  sides  of  the  vessel  are  surrounded  by  what 
is  called  a  "steam-jacket."  A  bent  tube  open 
at  both  ends  and  containing  mercury  in  the 
bend  is  sometimes  added.  When  the  mercury 
stands  at  the  same  level  in  both  arms,  the 
pressure  upon  the  surface  of  the  boiling  liquid 
is  just  equal  to  the  external  atmospheric  pres- 
sure, which  should  be  760  mm.  When  the 
mercury  column  has  come  to  rest,  a  mark  is 
made  on  the  glass  tube  at  the  level  of  the 
mercury.  This  point  is,  for  the  sake  of 
FIG.  238.  brevity,  called  the  boiling  point. 


308  TEMPERATURE. 

480.  Thermometric    Scales.  —  There   are    two 
scales  used  in  this   country,  the  centigrade  and 
Fahrenheit's.  For  these  scales,  the  fixed  points,  de- 
termined as  just  explained,  are  marked  as  follows  : 

Centigrade.  Fahrenheit. 

Freezing  point,          0°  32° 

Boiling  point,         100°  212° 

The  tube  between  these  two  points  is  divided 
into  100  equal  parts  for  the  centigrade  scale  and 
into  180  for  Fahrenheit's.  Hence  a  change  of 
temperature  of  5°  C.  is  equal  to  a  change  of  9°  F., 
or  an  interval  of  one  centigrade  degree  is  equal  to 
FIG.  239.  an  interval  of  -|  of  a  Fahrenheit  degree. 

481.  Thermometric    Readings.  —  To  change 
the  readings  of  a  centigrade  thermometer  to  those  of 
Fahrenheit's,  or  vice  versa,  is  a  little  more  complicated 
than  to  determine  the  relation  between  the  intervals  of 
temperature.     This  complication  arises  from  the  fact  that 
Fahrenheit's  zero  is  not  at  the  freezing  point  but  32  de- 
grees below.    To  reduce  Fahrenheit  readings  to  centigrade 
readings,  subtract  32  from  the  number  of  Fahrenheit  de- 
grees and  multiply  the  remainder  by  {. 


To  reduce  centigrade  readings  to  Fahrenheit  readings, 
multiply  the  number  of  centigrade  degrees  by  |  and  add  32. 

F.  =  |  0.  +  32. 
o 

(a.}  Suppose  that  we  desire  to  find  the  equivalent  centigrade 
reading  for  50°  F.  Subtracting  32,  we  see  that  this  temperature  is 
18  Fahrenheit  degrees  above  the  freezing  point.  But  one  Fahren- 
heit degree  being  equal  to  §  of  a  centigrade  degree,  this  temperature 


TEMPERATURE. 


309 


B  f  of  18,  or  10  centigrade  degrees  above  the  freezing  point.  Hence 
the  reading  will  be  10°  C. 

(6.)  Suppose  that  we  desire  to  find  the  equivalent  Fahrenheit 
reading  for  45°  C.  This  temperature  is  45  centigrade  degrees  above 
the  freezing  point,  or  81  Fahrenheit  degrees  above  the  freezing 
point.  Hence  the  reading  will  be  (81  +  32  =)  113°  F.  (See  Fig.  239.) 

(c.)  The  centigrade  thermometer  is  the  most  convenient  and  is 
adopted  in  all  countries  as  the  standard  scale  for  scientific  reference. 
Like  the  metric  system,  its  general  use  in  this  country  is  probably 
only  a  question  of  time. 

Note. — It  is  desirable  that  this  class  be  provided  with  several 
"  chemical "  thermometers ;  i.  e.,  thermometers  having  the  scale 
marked  on  the  glass  tube  instead  of  a  metal  frame. 

±82.  Differential  Thermometer.— Leslie's  dif- 
ferential thermometer  (Fig.  240)  shows  the  difference  in 
temperature  of  two  neighboring  places  by 
the  expansion  of  air  in  one  of  two  bulbs. 
These  bulbs  are  connected  by  a  bent  glass 
tube  containing  some  liquid  not  easily 
volatile.  It  is  an  instrument  of  simple 
construction  (See  Appendix,  M.)  and  great 
delicacy  of  action,  but  has  been  largely 
superseded  by  the  thermopile  and  galvan- 
ometer (§§414,391). 

483.    Expansion. — Heat    consists 
generally  of  molecular  vibrations.     What-        PIG.  240. 
ever   raises    the  temperature  of  a  body 
increases  the  energy  with  which  the  molecules  of  that 
body  swing  to  and  fro.    These  molecules  are  too  small  (§  5), 
and  their  range  of  motion  too  minute  to  be  visible,  and  we 
must  call  upon  our  imaginations  to  make  good  the  defect 
of  our  senses.     We  must  conceive  these  invisible  molecules 
as  held  together  by  the  force  of  cohesion,  yet  vibrating 
to  and  fro.    The  more  intense  the  heat,  the  greater  the 


310 


TEMPERATURE. 


energy  of  these  molecular  motions.  Molecules  thus  vi- 
brating must  push  each  other  further  apart,  and  thus  cause 
the  body  which  they  constitute  to  expand.  This  expansion, 
or  increase  of  volume,  is  the  first  effect  of  heat  upon 
bodies. 

(a.)  Imagine,  if  possible,  twenty-five  quiet  boys  standing  closely 
crowded  together.  Upon  the  floor  draw  a  chalk  line  enclosing  the 
group.  If  these  boys  be  suddenly  set  shaking,  as  by  the  ague,  they 
will  force  some  of  their  number  over  the  chalk  line.  From  the 
motions  of  the  individuals  has  resulted  an  expansion  of  the  living 
mass. 

484.  Expansion  Illustrated. — The  expansion  of 
solids  may  be  shown  by  a  ball,  which,  at  ordinary  tempera- 
tures, will  easily  pass  through  a 
ring ;  on  heating  the  ball  it  will 
no  longer  pass  through  the  ring. 
If  the  ball  be  cooled  by  plung- 
ing it  into  cold  water,  it  will 
again    pass  through    the    ring. 
This  illustrates  the  increase  of 
volume  or    cubical    expansion. 
Sometimes    the    expansion    in 
length  only  is  measured.     This 
is  called  linear  expansion.     Ex- 
pansion is  also  illustrated  in  the 

FIG.  241.  compensation  pendulum  (§  149). 

485.  Unequal  Expansion.— Different  substances 
expand  at  different  rates  for  the  same  change  of  temper- 
ature.     This  may  be  shown  by  heating  a  bar  made  by 
riveting  together,  side  by  side,  two  thin  bars  of  equal  size, 
one  of  iron  and  one  of  brass,  so  that  the  compound  bar 
shall  be  straight  at  the  ordinary  temperature.    As  brass 


TEMPERATURE.  311 

expands  and  contracts  more  than  iron,  when  the  compound 
bar  is  heated  it  will  curve  with  the  brass  on  the  convex 
side ;  when  it  is  cooled,  it  will  curve  with  the  brass  on  the 
concave  side. 

(a.)  Glass  and  platinum  expand  nearly  alike.  In  fact,  the  rates 
of  expansion  are  so  nearly  alike  that  platinum,  wires  may  be  fused 
into  glass  tubes,  as  is  done  in  electrolysis  apparatus  and  eudiometers. 
If  we  attempt  thus  to  fuse  copper  wire  into  glass,  the  glase  will  be 
broken  during  the  unequal  contraction  from  cooling. 

486.  Practical    Applications    of    Expansion. — The 

energy  of  expansion  and  contraction  of  solids,  when  heating  and 
cooling,  is  remarkable.  This  expansion  of  metals  by  heat  is 
utilized  by  coopers  in  setting  hoops,  by  wheelwrights  in  setting 
tires,  and  by  builders  in  straightening  bulging  walls.  When  the 
iron  rails  of  our  railways  are  laid,  a  small  space  is  left  between  the 
ends  of  each  two  adjoining  rails  to  provide  for  their  inevitable 
expansion  by  the  summer  heat.  The  iron  tubular  bridge  over  the 
Menai  Straits  is  about  1800  feet  long.  Its  linear  expansion  is  abort 
one  foot,  and  is  provided  for  by  placing  the  ends  of  the  huge  tube 
upon  rollers. 

487.  Expansion  of  Liquids. — The  expansion  of 
liquids  may  be  illustrated  as  follows :  Nearly  fill  a  Florence 
flask  with  water,  and  place  it  on  a  retort  stand  or  other 
convenient  support.    A  long  straw  is  supported  by  a  thread 
tied  near  one  end.    From  the  short  end  of  this  straw  lever 
is  suspended  a  weight  nearly  balanced  by  the  long  arm  of 
the  lever.     This  weight  hangs  in  the  neck  of  the  flask, 
and  rests  lightly  upon  the  surface  of  the  water  (§  238). 
By  placing  a  spirit-lamp  below  the  flask  the  water  may  be 
heated.     As  it  expands,  it  rises  in  the  neck  of  the  flask, 
raises  the  weight,  and  lowers  the  end  of  the  long  arm  of 
the  lever,  which  may  be  seen  to  move. 

488.  Anomalous   Expansion   of   Water. — 

Water  presents  a  remarkable  exception  to  the  general  rule. 
//  water  at  0°C.  be  heated,  it  will  contract  until  it 


312 


TEMPERA  TUBE. 


reaches  4°  C.,   Us  temperature  of  greatest  density. 
Heated,  above  this  point  it  expands. 

(a.)  Through  the  cork  of  a  large  flask  pass  a  fine  glass  tube.     Fill 
the  flask  with  water  at  the  ordinary  temperature,  and  insert  the 

cork  and  tube  so  that  the  water 
shall  rise  some  distance  in  the 
tube.  Place  the  flask  in  a  freezing 
mixture,  such  as  salt  and  pounded 
ice.  The  water  column  in  the 
tube  falls,  showing  that  the  water 
is  contracting.  But  before  the 
water  freezes  the  contraction 
ceases,  the  column  in  the  tube 
becomes  stationary,  and  then  be- 
gins to  rise  again.  This  shows 
that  water  does  not  contract  on 
being  cooled  below  a  certain  tem- 
perature, and  that  there  is  a  tem- 
perature of  maximum  density 
above  the  freezing  point. 

(&.)  Fig.  242  represents  a  glass 
cylinder  with  two  thermometers 
inserted  in  the  side,  near  the  top 
and  bottom,  at  A  and  B.  Midway 
between  A  and  B  is  an  envelope  O,  which  may  be  filled  with  a 
freezing  mixture.  The  envelope  being  empty,  the  cylinder  is  filled 
with  water  at  0°  C.,  and  placed  in  a  room  at  the  ordinary  temper- 
ature, about  15°C.  As  the  water  molecules  at  the  side  of  the 
cylinder  become  warm,  they  fall,  and  B  soon  records  a  temperature 
of  4°  0.,  while  A  remains  at  0°.  This  shows  that  the  warm  water 
falls  to  the  bottom.  It  falls  because  it  is  denser.  It  is  denser 
because  it  has  been  contracted  by  heat. 

If  the  experiment  be  varied  by  filling  the  cylinder  with  water  at 
the  ordinary  temperature,  and  C  with  a  freezing  mixture,  the  tem- 
perature at  B  will  fall  rapidly,  while  it  falls  slowly  at  A.  This 
will  continue  until  A  reaches  4°  C.,  when  A  begins  to  fall  more 
rapidly,  and  continues  to  do  so  until  it  reaches  0°.  These  experi- 
ments show  that  water  is  heavier  at  4°C.  than  at  any  temperature 
above  or  below. 

489.  Results  of  this  Exception. — This  prop- 
erty of  water  is  of  great  importance.  Were  it  otherwise, 


FIG.  242. 


TEMPERATURE. 


313 


the  ice  would  sink  and  destroy  everything  living  in  the 
water.  The  entire  body  of  water  would  soon  become  a 
solid  mass  which  the  heat  of  summer  could  not  wholly 
melt,  for,  as  we  shall  soon  see,  water  has  little  power  to 
carry  heat  downward.  As  it  is,  in  even  the  coldest  winters, 
the  mass  of  water  in  our  northern  lakes  remains  at  a  tem- 
perature of  4°C.,  the  colder  water  floats  upon  the  warmer 
layer,  ice  forms  over  all,  and  protects  the  living  things 
below. 

49O.  Expansion  of  Gases. — The  expansion  of 
gases  may  be  shown  by  partly  filling  a  bladder  with  cold 
air,  tying  up  the  opening,  and  placing  the  bladder  near 
the  fire.  The  expanded  air  will  fill  the  bladder.  Through 
the  cork  of  a  bottle  pass  a  small  glass  tube  about  a  foot 
long.  Warm  the  bottle  a  little  between  the  hands  and 
place  a  drop  of  ink  at  the  end  of  the  tube.  As  the  air 
contracts  the  ink  will  move  down  the  tube  and  form  a 
frictionless  liquid  index. 
By  heating  or  cooling  the 
bottle  the  index  may  be 
made  to  move  up  or  down. 
If  a  closed  flask  having  a 
delivery  tube  terminating 
under  water  be  heated, 
some  of  the  expanded  air 
will  be  forced  to  escape, 
and  may  be  seen  bubbling 
through  the  water.  By 
"collecting  over  water" 
the  air  thus  driven  out, 
it  may  be  accurately 
measured.  (Fig.  243.) 

14: 


FIG.  243. 


314  TEMPERA  TUBE. 

* 

49  1  .  Practical  Results.—  The  ascension  of  '  '  fire-balloons  " 
and  the  draft  of  chimneys  are  due  to  the  expansion  of  gases  by  heat. 
When  the  air  in  the  chimney  of  a  stove  or  lamp  is  heated,  it  is  ren- 
dered lighter  than  the  same  bulk  of  surrounding  air,  and,  therefore, 
rises.  The  cooler  air  comes  in  to  take  its  place  and  thus  feeds  the  com- 
bustion. Sometimes  when  a  fire  is  first  lighted,  the  chimney  is  so 
cold  that  the  current  is  not  quickly  established  and  the  smoke 
escapes  into  the  room.  But  in  a  little  while  the  air  column  rises 
and  the  usual  action  takes  place.  By  the  aid  of  a  good  thermometer 
it  may  be  shown  that  the  air  near  the  ceiling  of  a  room  is  warmer 
than  the  air  near  the  floor.  When  the  door  of  a  warmed  room  is 
left  slightly  ajar,  there  will  be  an  inward  current  near  the  floor  and 
an  outward  current  near  the  top  of  the  door.  These  currents  may 
be  shown  by  holding  a  lighted  candle  at  these  places.  Artificial 
ventilation  depends  upon  the  same  principles. 

492.  Rate  of  Gaseous  Expansion.—  The  rate 
of  expansion  is  practically  the  same  for  all  gases,  viz., 
0.00336  or  ^  of  the  volume  at  0°  0.,  for  each  centigrade 
degree  that  the  temperature  is  raised  above  the  freezing 
point.  In  other  words,  a  liter  of  air  at  0°  C.,  expands  to 

11  +  .00336  I  at  1°  C., 
11+  (.00338  x  2)  I  at  2°  C. 

Of  course,  if  we  use  Fahrenheit  degrees  the  expansion 
will  be  only  £  as  great,  or  about  ?fa.  A  litre  of  gas  at  32°  F. 
expands  to  Ijfo  I  at  33°  F.  ;  to  ffl  I  at  39°  F.,  etc. 


11+  (.00336  x  3)?.  at  3°  C., 
I  at  4°  C. 


493.  Absolute  Zero  of  Temperature.—  The 

temperature  at  which  the  molecular  motions  con- 
stituting heat  wholly  cease  is  called  the  absolute 
zero.  It  has  never  been  reached,  and  has  been  only  ap- 
proximately determined,  but  it  is  convenient  as  an  ideal 
starting-point.  The  zero  point  of  the  thermometers  does 
not  indicate  the  total  absence  of  heat.  A  Fahrenheit 
thermometer,  therefore,  does  not  indicate  that  boiling 
water  is  212  times  as  hot  as  ice  at  1°  F.  ;  a  centigrade 


TEMPERA  TURE.  315 

thermometer  does  not  indi^te  that  boiling  water  has  100 
times  as  much  heat  as  water  at  1°  C. 

(a.)  Temperature,  when  reckoned  from  the  absolute  zero,  is  called 
absolute  temperature.  Absolute  temperatures  are  obtained  by  add- 
ing 460  to  the  reading  of  a  Fahrenheit  thermometer,  or  273  to  the 
reading  of  a  centigrade  thermometer. 

494.  Temperature,  Volume  and  Pressure. — 

By  raising  a  gas  from  0°  C.  to  273°  C.,  its  volume  will  be 
doubled.  To  reduce  the  gas  at  this  temperature  to  its 
original  volume,  the  original  pressure  must  be  doubled. 
From  our  knowledge  of  pneumatics  and  gaseous  expansion, 
we  are  able  to  solve  certain  problems  relating  to  the  volume 
of  gases  under  different  pressures  and  temperatures. 

Examples. — (1.)  A  mass  of  air  at  0°  C.  and  under  an  atmos- 
pheric pressure  of  30  inches,  measures  100  cu.  inches  ;  what  will  be 
its  volume  at  40°  C.  under  a  pressure  of  28  inches  ?  First,  suppose 
the  pressure  to  change  from  30  inches  to  28  inches.  The  air  will 
expand,  the  two  volumes  being  in  the  ratio  of  28  to  30  (§  284).  In 
other  words,  the  volume  will  be  f  f  times  100  cubic  inches  or  107  \ 
cu.  in.  Next,  suppose  the  temperature  to  change  from  0°  C.  to 
40°  C.  The  expansion  will  be  -gfo  of  the  volume  at  0°  C. ;  the  volume 
will  be  1¥\°3  of  the  volume  at  0°  C.  1/T°¥  times  107|  cubic  inches 
=122 |ff  inches.— Ans. 

The  problem  may  be  worked  by  proportion  as  follows  : 
28  :  30 


OQ    .        QA 

01  £  ;  273  +  40 

(2.)  At  150°  C.,  what  will  be  the  volume  of  a  gas  that  measures 
10  cu.  cm.  at  15°  C.  ? 

273  +  15  :  273  +  150  : :  10  :  x,          .'.  x  =  14.69  cu.  cm. 

(3.)  If  100  cu.  cm.  of  hydrogen  be  measured  at  100°  C. ,  what  will 
be  the  volume  of  the  gas  at  —100°  C.? 

273  +  100  :  273  -  100  : :  100  :  a-.      .'.  x  =  40.37  cu.  cm. 


316  TEMPERATURE. 

(4.)  A  liter  of  air  is  measured  at  0°  C.  and  760  mm.   What  volume 
will  it  occupy  at  740  mm.,  and  15.5°  C.  ? 

+ 


740     760  :  l>m  ''  *'        V  X  =  1085'34  cu'  cm' 

EXERCISES.    .  „,  , 

1.  A  rubber  balloon,  capacity  of  1  liter,  contains  900  cu.  cm.  of 
oxygen  at  0°  C.     When  heated  to  30°  C.,  what  will  be  the  volume 
of  the  oxygen  ?  Am.  998.9  cu.  cm. 

2.  If  170  volumes  of  carbonic  acid  gas  be  measured  at  10°  C.,  what 
will  be  the  volume  when  the  temperature  sinks  to  0°  C.  ? 

3.  A  certain  weight  of  air  measures  a  liter  at  0°  C.    How  much 
will  the  air  expand  on  being  heated  to  100°  C.  ? 

4.  A  gas  has  its  temperature  raised  from  15°  C.  to  50°  C.     At  the 
latter  temperature  it  measures  15  liters.     What  was  its  original 
volume  ? 

5.  A  gas  measures  98  cu.  in.  at  185°  F.    What  will  it  measure  at 
10°  C.  under  the  same  pressure  ? 

6.  To  what  volume  will  a  liter  of  gas  contract  in  cooling  from 
42°  F.  to  32°  F.  ?  Ans.  980  cu.  cm. 

7.  A  certain  quantity  of  gas  measures  155  cu.  cm.  at  10°  C.,  and 
under  a  barometric  pressure  of  530  mm.     What  will  be  the  volume 
at  18.7°  C.,  and  under  a  barometric  pressure  of  590  mm.1 

8.  A  gallon  of  air  (231  cu.  in.}  is  heated,  under  constant  pressure, 
from  0°  C.  to  60°  C.     What  was  the  volume  of  the  air  at  the  latter 
temperature  ? 

9.  A  fire  balloon  contains  20  cu.  ft.  of  air.     The  temperature  of 
the  atmosphere  being  15°  C.,  and  that  of  the  heated  air  in  the  bal- 
loon being  75°  C.  ,  what  weight,  including  the  balloon,  may  be  thus 
supported?    (See  Appendix  G.) 

10.  The  difference  between  the  temperatures  of  two  bodies  is 
36°  F.    Express  the  difference  in  centigrade  degrees. 

11.  The  difference  between  the  temperatures  of  two  bodies  is 
35°  C.    Express  the  difference  in  Fahrenheit  degrees. 

12.  (a.)  Express  the  temperature  68°  F.  in  the  centigrade  scale. 
(&.)  Express  the  temperature  203  C.  in  the  Fahrenheit  scale. 

13.  What  will  be  the  tension  at  30°  C.  of  a  quantity  of  gas  which 
at  0°  C.  has  a  tension  of  a  million  dynes  per  sq.  cm.,  the  volume 
remaining  the  same  ?    (§  69.)  Ans.  1109800  dynes. 

14.  A  liter  of  gas  under  a  pressure  of  1013600  dynes  per  sq.  cm. 
is  allowed  to  expand  until  the  pressure  is  reduced  to  1000000  dynes 
per  sq.  cm.    At  the  same  time,  the  temperature  is  raised  from  0°  C 
to  100°  C.    Find  the  final  volume.     A  ns.  1385  cu.  cm.  nearly. 


LIQUEFACTION.  317 

Recapitulation.— In  this  section  we  have  considered 
the  Nature  of  Heat;  the  meaning  of  Tem- 
perature ;  Thermometers  and  their  graduation ; 
the  determination  of  the  Freezing  and  Boiling 
Points;  thermometric  Scales  and  Readings; 
the  Differential  Thermometer  ;  Expansion 
of  Solids  ;  Expansion  of  Liquids,  especially 
the  Expansion  of  Water  ;  the  Expansion  of 
Gases  and  the  Rate  thereof;  Absolute  Zero  of 
temperature;  the  relation  between  Temperature, 
Pressure  and  Volume. 


ECTfON  il. 


LIQUEFACTION,    VAPORIZATION,    DISTILLATION. 

495.  Liquefaction. — In  the  last  section  we  learned, 
that  heat  is  a  form  of  energy.  As  energy,  it  is  able  to 
perform  work,  such  as  overcoming  or  weakening  the  force 
of  cohesion.  It  is  well  known  that  when  a  solid  is  changed 
to  the  liquid  or  aeriform  condition,  or  when  a  liquid  is 
changed  to  a  vapor,  it  is  done  by  an  increase  of  heat,  and 
that  when  the  reverse  operations  are  performed,  it  is  by  a 
diminution  of  heat.  Cohesion  draws  the  particles  together ; 
heat  pushes  them  asunder,  and  on  the  varying  preponder- 
ance of  one  or  the  other  of  these  antagonistic  powers,  the 
condition  of  the  body  seems  to  depend.  When  the  firm 
grip  of  cohesion  has  been  so  far  weakened  by  heat  that  the 
molecules  easily  change  their  relative  positions  (§  55),  the 
body  passes  from  the  solid  into  the  liquid  condition.  This 
change  of  condition  is  called  liquefaction. 


318 


LIQUEFACTION. 


496.  Laws  of  Fusion. — It  has  been  found  by 
experiment  that  the  following  statements  are  true : 

(1.)  Every  solid  begins  to  melt  at  a  certain  temperature 
which  is  invariable  for  the  given  substance  if  the  pressure 
be  constant.  When  cooling,  the  substance  will  solidify  at 
the  temperature  of  fusion. 

(2.)  The  temperature  of  the  solid,  or  liquid,  remains  at 
the  melting  point  from  the  moment  that  fusion  or  solidi- 
fication begins  until  it  is  complete. 

(a.)  If  a  flask  containing  ice  be  placed  over  a  fire,  it  will  be  found 
that  the  hotter  the  fire  the  more  rapid  the  liquefaction,  but  that  if 
the  contents  of  the  flask  be  continually  stirred,  the  thermometer 
will  remain  at  0°  C.  until  the  last  bit  of  ice  is  melted  (§  478).  If 
sulphur  be  used  instead  of  icCj  the  tem- 
perature will  remain  at  115°C.  until  the 
sulphur  is  all  melted.  (Fig.  244.) 

497.  Reference  Table  of  Melt- 
ing Points : 

Alcohol,     -    -    -    ..       Never  frozen. 
Mercury,      ....        — 38.8°C. 
Sulphuric  acid,   -     -  — 344 

Ice, -  0. 

Sulphur,    ---     -  115. 

Lead,        -     -     -    -  326 

Zinc,      ....  425 

Silver  (pure),     -    -  1,000 

Gold  (pure),    -     -  1,250 

Iron  (wrought),      -     -       1,600 
Mote. — The  higher  temperatures  in  this 
244.  table    are    only    approximate.       Certain 

bodies  soften  and  become  plastic  before  they  melt.     In  this  condition 

glass  is  worked  and  iroii  is  welded. 

498.  Vaporization.— If,  after  liquefaction,  further 
additions  of  heat  be  made,  a  point  will  be  reached  at  which 
the  heat  will  overbalance  both  the  cohesion  and  the 
pressure  of  the  atmosphere  and  the  liquid  pass  into  the 
aeriform  condition.  This  change  of  form  is  called  vapor- 


VAPORIZATION. 


319 


ization.    Vaporization  may  be  of  two  kinds— evaporation 
and  ebullition. 

499.  Evaporation. — Evaporation    signifies  the 
quiet   formation    of   vapor    at    the    surface    of    a 
liquid. 

(a.)  With  reference  to  the  rapidity  with  which  evaporation  takes 
place,  it  may  be  remarked  that— 

(1.)  It  varies  with  the  temperature. 
(2.)  It  varies  with  the  extent  of  surface. 

(3.)  It  varies  with  pressure  upon  the  liquid,  being  exceedingly 
rapid  in  a  vacuum. 

500.  Evaporation  in  Vacuo. — The  rapid  forma- 
tion of  vapors  in  a  vacuum  is  prettily  illustrated  by  the 
following     experiment  : 

Torricellian  vacua  are 
formed  at  the  top  of  four 
barometer  tubes,  A,  B, 
G  and/),  Fig.  245.  Into 
the  mouth  of  B  pass  a 
few  drops  of  water.  They 
will  rise  through  the  mer- 
cury to  the  vacuum  at 
the  top.  Upon  reaching 
this  open  space  they  are 
instantly  vaporized.  The 
tension  of  the  aqueous 
vapor  shows  itself  by 
lowering  the  mercury 
column.  This  depression 
is  due  to  the  tension 
rather  than  to  the  weight 
of  the  vapor,  because  the 
water  weighs  scarcely  anything  compared  with  the  mer- 


320 


VAPORIZATION. 


oury  it  displaces.  Introducing  the  same  quantity  of 
alcohol  into  C3  and  of  ether  into  D,  they  are  instantly 
vaporized,  but  the  mercury  will  be  depressed  more  by  the 
alcohol  than  by  the  water,  and  more  by  the  ether  than  by 
the  alcohol. 

(a.)  At  the  beginning  of  the  experiment,  the  four  mercury 
columns  indicated  the  atmospheric  pressure;  at  the  end  of  the 
experiment,  the  column  in  A  indicated  the  full  pressure  of  the 
atmosphere  ;  the  columns  in  B,  C  and  D  indicate  that  pressure 
minus  the  tension  of  their  respective  vapors.  This  experiment 
also  shows  that,  at  the  same  temperature,  tlw  vapors  of  different 
liquids  have  different  tensions, 

501.  Ebullition. — Ebullition,  or  boiling,  signi- 
fies the  rapid  formation  of  vapor  bubbles  in  the 

mass  of  a  liquid. 
When  a  flask  con- 
taining water  is 
placed  over  the  flame 
of  a  lamp,  the  ab- 
sorbed air  that  is 
generally  to  be  found 
in  water  is  driven  off 
in  minute  bubbles 
that  rise  and  escape 
without  noise.  As 
the  temperature  of 
the  water  is  raised, 
the  liquid  molecules 
in  contact  with  the 
bottom  of  the  flask 

become  so  hot  that 
FIG.  246.  . 

the  heat  is  able  to 

overcome  the  cohesion  between  the  molecules,  the  pressure 


VAPORIZATION.  321 

of  the  overlying  water,  and  the  pressure  of  the  atmosphere 
above  the  water.     Then  the  water  boils. 

(a.)  When  the  first  bubbles  of  steam  are  formed  at  the  bottom  of 
the  water,  they  rise  through  the  water,  condense  in  the  cooler  layers 
above,  and  disappear  before  reaching  the  surface.  The  formation 
and  condensation  of  these  bubbles  produce  the  peculiar  sound  known 
as  singing  or  simmering,  the  well-known  herald  of  ebullition. 
Finally,  the  water  becomes  heated  throughout,  the  bubbles  increase 
in  number,  grow  larger  as  they  ascend,  burst  at  the  surface,  and 
disappear  in  the  atmosphere.  The  whole  liquid  mass  is  agitated 
with  considerable  vehemence,  there  is  a  characteristic  noisy  accom- 
paniment, the  quantity  of  water  in  the  flask  diminishes  with  every 
bubble,  and  finally  it  all  disappears .  as  steam.  The  water  has 
"boiled  away." 

502.  Laws  of  Ebullition. — It  has  been  found  by 
experiment  that  the  following  statements  are  true : 

(1.)  Every  liquid  begins  to  boil  at  a  certain  temperature, 
which  is  invariable  for  the  given  substance  if  the  pressure 
be  constant.  When  cooling,  the  substance  will  liquefy  at 
the  temperature  of  ebullition,  or  at  the  boiling  point. 

(2.)  The  temperature  of  the  liquid,  or  vapor,  remains 
at  the  boiling  point  from  the  moment  that  it  begins  to 
boil  or  liquefy. 

(3.)  An  increase  of  pressure  raises  the  boiling  point;  a 
decrease  of  pressure  lowers  the  boiling  point. 

503.  Effect  of  Pressure  upon  Boiling  Point. 

We  saw  in  §  501  that  when  a  liquid  is  boiled,  the  heat 
has  three  tasks  or  three  kinds  of  work  to  perform,  viz., 
overcoming  cohesion,  liquid  and  atmospheric  pressures. 
Nothing  can  be  more  evident  than  the  propositions  that 
increasing  the  work  to  be  done  involves  an  increase  in  the 
energy  needed  to  do  the  work ;  that  decreasing  the  work 
to  be  done  involves  a  decrease  in  the  energy  needed  to  do 
the  work.  In  the  case  of  boiling  any  given  liquid,  the  first 


322  VAPORIZATION. 

of  the  three  tasks  can  not  be  varied ;  either  of  the  other 
two  easily  may.  If  we  increase  the  pressure  we  increase 
the  work  to  be  done,  and  therefore  increase  the  necessary 
amount  of  heat,  the  only  form  of  energy  competent  to  do 
the  work.  If  we  lower  the  pressure  we  lessen  the  work  to 
be  done,  and  therefore  lessen  the  necessary  amount  of 
heat.  This  means.,  in  the  first  case,  raising  the  boiling 
point;  in  the  second  case,  lowering  the  boiling  point. 

5O4.  Franklin's  Experiment.— The  boiling  of 
water  at  a  temperature  below  100°  C.  may  be  shown  as 
follows:  Half  fill  a  Florence  flask  with  water.  Boil  the 
water  until  the  steam  drives  the  air  from  the  upper  part 
of  the  flask.  Cork  tightly,  remove  the  lamp  and  invert 
the  flask.  The  exclusion  of  the  air  may  be  made  more 
certain  by  immersing  the  corked  neck  of  the  flask  in  water 
that  has  been  recently  boiled.  When  the  lamp  was  re- 
moved the  temperature  was  not  above  100°  C.  By  the 

time  that  the  flask  is  in- 
verted and  the  boiling 
bas  ceased  the  tempera- 
ture will  have  fallen  be- 
low 100°  C.  When  the 
boiling  stops,  pour  cold 
water  upon  the  flask ;  di- 
rectly the  boiling  begins 
again. 

(a.)  The  cold  water  poured 
upon  the  flask  lowers  the 
temperature  of  the  water  in 
the  flask  still  further,  but  it 
also  condenses  some  of  the 
steam  in  the  flask  or  reduces 
FIG.  247  its  tension  (§494).  This  re- 


VAPORIZA  TION. 


323 


duction  of  the  tension  lessens  the  work  necessary  to  boiling.  There 
being  enough  heat  in  the  water  to  do  this  lessened  amount  of  work, 
the  water  again  boils  and  increases  the  pressure  until  the  boiling 
point  is  raised  above  the  present  temperature  of  the  water.  The 
flask  may  be  drenched  and  the  water  made  to  boil  a  dozen  times  in 
succession  with  a  single  heating.  The  experiment  may  be  made 
more  striking  by  plunging  the  whole  flask  under  cool  water. 

5O5.  The  Culinary  Paradox. — The  same  prin- 
ciple may  be  illustrated  by  the  apparatus  represented  in 
Fig.  248.  The  re- 
ceiver R,  having 
been  exhausted  with 
an  air  -  pump,  is 
closed  by  the  stop- 
cock s.  The  flask  F 
is  half  full  of  water 
and  heated  by  a 
lamp  placed  be- 
neath. As  the  water 
boils,  the  steam  es- 
capes through  the 
open  stop-cocks  a 
and  c.  When  the  steam  has  expelled  the  air  from  F, 
close  a  and  c,  removing  the  lamp  at  the  same  time. 
The  water  gradually  cools  and  ceases  to  boil.  Water  may 
be  dashed  over  F  and  the  water  made  to  boil  as  in  the  last 
experiment.  When  this  has  been  done  a  few  times,  the 
water  may  he  allowed  to  come  to  rest.  It  will  be  several 
degrees  below  the  boiling  point.  Opening  a  and  s,  the 
vapor  of  F  escapes  into  R  and  the  water  begins  to  boil 
vigorously.  By  keeping  R  cool,  the  water  in  F  may  be 
made  to  boil  for  a  considerable  time. 

5O6.   Papin's  Digester. — At  high  elevations  water  boils  at 
a  temperature  too  low  for  culinary  purposes.     Persons  living  there 


FIG.  248. 


324 


VAP  ORIZA  TION. 


are  obliged  to  boil  meats  and  vegetables  (if  at  all)  in  closed  vessels 
and  under  a  pressure  greater  than  that  of  the  atmosphere.  In  the 
arts,  a  higher  temperature  than  100°  C.  is  sometimes  required  for 
water,  as,  for  example,  in  the  extraction  of  gelatine  from  bones.  In 
a  closed  vessel,  water  may  be  raised  to  a  much  higher  temperature 
than  in  the  open  air,  but,  for  reasons  now  obvious,  water  cannot  be 
kept  boiling  in  such  a  vessel.  Papin's  Digester  consists  of  a  metal 
vessel  of  great  strength  covered  with  a  lid  pressed  down  by  a 
powerful  screw.  That  the  joint  may  be  more  perfect,  a  ring  of 
sheet  lead  is  placed  between  the  edges  of  the  cover  and  of  the  vessel. 
It  is  provided  with  a  safety  valve,  pressed  close  by  a  loaded  lever. 
When  the  tension  of  the  steam  reaches  a  dangerous  point,  it  opens 
the  valve,  lifting  the  weight,  and  thus  allows  some  of  the  steam 
to  escape. 

5O7.  Marcet's  Globe.— Marcet's  globe  is  represented 
in  Fig.  249.  It  consists  of  a  spherical  metallic  boiler,  five 
or  six  inches  in  diameter,  provided  with  three  openings, 
through  one  of  which  a  thermometer,  T,  passes ;  through 
the  second  of  which  a  glass  manometer  tube,  M,  passes ;  the 
third  opening  being  provided  with  a  stop-cock,  S.  The 
thermometer  and  manometer  tubes  fit  their  openings  so 
closely  that  no  steam  can  escape  at  those  points.  The 
thermometer  bulb  is  exposed  directly  to 
the  steam.  The  lower  end  of  the  manometer 
tube  dips  into  mercury  placed  in  the  lowei 
part  of  the  globe.  The  boiler  is  to  be  half 
filled  with  water  and  heated  until  the 
water  boils,  the  stop-cock  being  open.  As 
long  as  the  stop-cock  is  open,  the  ther- 
mometer will  not  rise  above  100°  C.  When 
the  stop-cock  is  closed,  the  steam  accumu- 
lates, the  pressure  on  the  water  increases, 
the  thermometer  shows  a  rise  of  temperature 
beyond  100°  C.  higher  and  higher  as  the 
FIG  2  mercury  rises  in  the  manometer  tube. 


VAPORIZATION.  325 

When  the  mercury  in  the  manometer  tube  is  760  mm. 
above  the  level  of  the  mercury  in  the  boiler,  the  steam 
has  a  tension  of  two  atmospheres,  and  the  thermometer 
will  record  a  temperature  of  about  121°  C. 

508.  Concerning    Steam. — A  given  mass  of 
water  in  the   aeriform  condition  occupies  nearly 
1700  times  as  much  space  under  a  pressure  of 
one  atmosphere  as  it  does  in  the  liquid  condition. 
In  other  words,  a  cubic  inch  of  water  will  yield  nearly  a 
cubic  foot  of  steam.     Steam   is   invisible.     What  is 
commonly  called  steam  is  not  true  steam,  but  little  globules 
of  water  condensed  by  the  cold  air  and  suspended  in  it. 
By  carefully  noticing  the  steam  issuing  from  the  spout  of 
a  tea-kettle,  it  will  be  observed  that  for  about  an  inch  from 
the  spout  there  is  nothing  visible.     The  steam  there  has 
not  had  opportunity  for  condensation.     The  water  particles 
visible  beyond  this  space  passed  through  it  as  invisible 
steam.    The  steam  in  the  flask  of  Fig.  247  and  in  F  of 
Fig.  248  is  invisible 

509.  Reference  Tables.— Boiling  Points  under  a  pressure 
of  one  atmosphere : 

Alcohol..  .    78°  C. 


Ammonia —40°  C. 

Sulphurous  anhydride.  ..—  8 

Ether 35 

Carbon  bisulphide 48 


Water  (pure) 100 

Mercury 350 

Sulphur 447 


Some  solids,  as  iodine,  arsenic  and  camphor  vaporize  without 
visible  intermediate  liquefaction.     The  process  is  called  sublimation. 

Boiling  Points  of  water  at  different  pressures : 

Atmospheres. 
1 
2 
3 
6 

10 
20 


Thermometer. 

Barometer. 

Thermometer. 

184°  F. 

16.676  inches 

212°  F. 

190 

18.992 

249.5 

200 

23.454 

2733 

210 

28.744 

318.2 

212 

29.922 

356.6 

215 

31.730 

415.4 

326 


VAPORIZA  TION. 


I 


510.  Definition  of  Boiling  Point.— We  ought 
now  to  be  fully  prepared  to  understand  that  the  boiling 
point  of  a  liquid  is  the  temperature  at  which  it 

gives  off  a  vapor  of  the  same 
tension  as  the  surrounding  at- 
mosphere. 

(a.)  If  there  be  any  doubt  or  lack  of 
comprehension  of  this  proposition,  it  may 
be  removed  by  the  following  experiment : 
A.  A  glass  tube,  bent  as  shown  at  A,  fcas  its 
short  arm  closed  and  its  long  arm  open. 
The  short  arm  is  nearly  filled  with  mer- 
cury, the  space  above  the  mercury  being 
filled  with  water.  While  water  is  briskly 
boiling  in  a  flask,  the  bent  tube  is  sus- 
pended in  the  steam,  as  shown  in  Fig. 
250.  Part  of  the  water  in  the  bent  tube 
is  changed  to  vapor,  the  mercury  falls  in 
the  short  arm,  and  finally  assumes  the  same 
FIG.  250.  level  in  both  branches. 

511.  Distillation. — Distillation  is  a  process  of  sep- 
arating a  liquid  from  a  solid  which  it  holds  in  solution,  or 
of  separating  a  mixture  of  two  liquids  having  different 
boiling  points.     The  process  depends  upon  the  fact  that 
different  substances  are  vaporized  at  different  temperatures. 
The  apparatus,  called  a  still,  is  made  in  many  forms,  but 
consists  essentially  of  two  parts — the  retort  for  producing 
vaporization,  and  a  condenser  for  changing  the  vapor  back 
to  the  liquid  form.     Fig.  251  represents  one  form  of  the 
apparatus.    It  consists  of  a  retort,  ab,  the  neck  of  which  is 
connected  with  a  spiral  tube,  dd,  called  the  worm.     The 
worm  is  placed  in  a  vessel  containing  water.     This  vessel 
is  continually  fed  with  cold  water  carried  to  the  bottom  by 
the  tube  h.     As  the  water  is  warmed  by  the  worm  it  rises 
and  overflows  at  i. 


DISTILL  A  TION. 

1  I 


FIG. 251. 

512.  Distillation  of  a  Liquid  from  a  Solid. 

—Suppose  that  water  is  to  be  separated  from  the  salt  it 
holds  in  solution.  The  brine  is  placed  in  a  retort  and 
heated  a  little  above  212°  F.  At  this  temperature  the 
water  is  vaporized  while  the  salt  is  not.  The  steam  is 
driven  from  the 
retort  through  the 
worm,  where  it  is 
rapidly  condensed 
and  passes  into  a 
vessel  prepared  to 
receive  it.  The 
salt  remains  in 
the  retort.  Of 
course,  the  water  B= 
of  the  vessel  con- 
taining the  worm  FIG.  252. 


328  DISTILLATION. 

must  be  kept  cool.  This  is  done  by  constantly  feeding  it 
at  the  bottom  with  cold  water,  as  explained  in  the  last 
article. 

(a. )  Fig.  252  represents  a  simpler  form  of  apparatus  for  this  pur- 
pose. The  retort  is  a  Florence  flask,  the  delivery  tube  of  which 
passes  through  a  "water-jacket."  The  method  of  supplying  this 
condenser  with  cold  water  is  evident  from  the  figure.  Sometimes 
the  delivery  tube  passes  directly  into  a  vessel  placed  in  a  cold  water 
bath,  this  vessel  serving  as  both  condenser  and  receiver. 

513.  Distillation  of  a  Liquid  from  a  Liquid. 

— Suppose  that  alcohol  is  to  be  separated  from  water. 
The  solution  is  placed  in  the  retort  and  heated  to  about 
90°  C.,  which  is  above  the  boiling  point  of  alcohol  but 
below  that  of  water.  The  alcohol  will  pass  over  in  a  state 
of  vapor  and  be  condensed,  while  the  water,  etc.,  remains 
behind.  In  practice,  the  alcohol  vapor  passes  over  charged 
with  a  certain  amount  of  steam.  A  receiver  placed  in  a 
bath  containing  boiling  water  is  interposed  between  the 
retort  and  the  worm  or  condenser.  In  this  receiver  the 
steam  condenses,  while  the  vapor  of  alcohol  passes  on  to 
the  worm  where  it  also  is  condensed.  This  process  is  known 
as  "fractional  distillation.'5 

Recapitulation. — In  this  section  we  have  considered 
the  meaning  of  Liquefaction  ;  the  Laws  of  Fu- 
sion ;  the  meaning  and  kinds  of  Vaporization  ; 
Evaporation  in  air  and  in  vacuo  ;  Ebullition  and 
its  Laws;  effect  of  Pressure  upon  the  boiling  point; 
Steam  ;  definition  of  Boiling  Point ;  Distilla- 
tion. 


LATENT   AND    SPECIFIC    HEAT.  329 


EGT1ON  III. 


LATENT    AND    SPECIFIC    HEAT. 

514.  Thermal  Units. -In  §  473  it  was  stated  that 
heat  is  measurable;  but  that  we  may  measure  it,  a  standard 
or  unit  of  measure  is  necessary.    A  thermal  or  heat 
unit  is  the  amount  of  heat  necessary  to  warm  a 
weight  unit  of  water  one  degree  above  the  freezing 
point.    The  weight  unit  generally  used  is  the  kilogram  or 
pound;   any  other  weight  unit  may  be  used  with  equal 
propriety.     The  degree  may  be  centigrade  or  Fahrenheit. 

(a.)  We  therefore  have  at  least  four  units  in  common  use.  They 
are  the  amounts  of  heat  necessary  to  warm 

(1.)  A  kilogram  of  water  from  0°  C.  to  1°  C. 
(2.)  A  kilogram  of  water  from  32°  F.  to  33°  P. 
(3.)  A  pound  of  water  from  0°  C.  to  1°  C. 
(4.)  A  pound  of  water  from  32°  F.  to  33°  F. 

It  makes  no  practical  difference  which  unit  is  used,  excepting  so 
far  as  convenience  is  concerned,  but  the  unit  must  not  be  changed 
during  any  problem.  The  first  of  these  units  is  called  a  calorie. 

515.  Two  Fruitful  Questions. — We  have  already  seen 
that  heat  melts  ice,  and  that  during  the  melting  the  temperature  i& 
constant ;   that  heat  boils  water,  and  that  durisg  the  boiling  the 
temperature  is  constant.     One  feature  of  this  change  of  condition 
remains  to  be  noticed  more  fully.     Take  a  block  of  ice  with  a  tem- 
perature of  —10°  C.  (14°  F.)  and  warm  it.     A  thermometer  placed  in 
it  rises  to  0°  C.     The  ice  begins  to  melt,  but  the  mercury  no  longer 
rises.     Heat  is  still  applied,  but  there  is  no  increase  of  temperature ; 
the  mercury  in  the  thermometer  remains  stationary  until  the  last 
particle  of  ice  has  been  liquefied.     Then,  and  not  till  then,  does  the 
temperature  begin  to  rise.     It  continues  to  do  so  until  the  ther- 
mometer marks  100°  C.     The  liquid  then  begins  to  boil,  and  the 
temperature  a  second  time  becomes  fixed.     But  during  all  the  time 
that  the  thermometer  stood  at  0°  C. ,  or  while  the  ice  was  melting, 
heat  was  given  by  the  lamp  and  received  by  the  ice.     Why  then  did 
not  the  temperature  rise  during  that  time,  instead  of  remaining  the 


330  *     LATENT  AND  SPECIFIC  HEAT. 

same  until  the  last  particle  of  ice  was  melted?  After  the  water 
began  to  boil,  heat  was  continuously  supplied.  Why  then  was 
there  not  a  continued  increase  of  temperature  ? 

516.  Molecular  Energies. — Heat  is  a  form  of  energy  and 
maybe  kinetic  or  potential.     There  can  be  no  doubt  that  when  a 
body  is  heated  its  molecules  are  thrown  into  violent  motion,  and 
that  as  the  temperature  is  raised  the  energy  of  this  molecular  motion 
is  increased,  or  that  as  this  molecular  motion  is  increased,  the  tem- 
perature is  raised.     But  some  of  this  molecular  energy  that  we  call 
heat,  instead  of  being  used  to  set  the  molecules  of  the  body  in  motion, 
has  work  of  a  different  kind  to  perform.     That  part  of  the  heat 
which  is  spent  in  producing  molecular  vibrations,  which  increases 
the  temperature,  is  called  sensible  heat.     Another  part  is  employed 
in  pushing  the  molecules  of  the  body  asunder,  producing  expansion 
and  change  of  condition.     In  forcing  these  molecules  asunder,  in- 
visible energy  of  motion  is  changed  to  energy  of  position  as  truly 
and  as  necessarily  as  visible  energy  of  motion  is  changed  to  the 
potential  variety  in  throwing  or  carrying  a  stone  from  the  earth  to 
the  house-top.    (§  159.) 

517.  Transmutation  of  Molecular  Energy.— In  most 
cases,  but  little  of  the  heat  communicated  to  a  body  is  thus  changed 
to  potential  energy,  the  greater  part  remaining  energy  of  motion 
and  increasing  the  temperature.    But  there  are  certain  crises,  or 
"  critical  occasions,"  on  which  the  greater  part  of  the  heat  communi- 
cated is  transformed  into  energy  of  position.     Thus,  at  the  melting 
point,  a  large  quantity  of  heat  maybe  given  to  ice  without  affecting 
the  temperature  at  all ;  instead  of  raising  the  temperature,  it  merely 
melts  the  ice.    The  energy  used  has  been  changed  from  the  kinetic 
to  the  potential  variety.     In  like  manner,  at  the  boiling  point,  a 
large  quantity  of  heat  may  be  given  to  the  water  without  affecting 
the  temperature  at  all.    Instead  of  raising  the  temperature  further, 
it  merely  vaporizes  the  water,  and  the  steam  has  the  same  tempera- 
ture as  the  water  from  which  it  came.     The  same  change  of  molec- 
ular energy  of  motion  into  molecular  energy  of  position  has  again 
taken  place.     This  heat,  which  is  thus  used  to  overcome  cohesion 
and  change  the  condition  of  matter,  does  not  affect  the  temperature 
and  therefore  is  not  sensible,  but  is  stored  up  as  potential  energy 
and  thus  hidden  or  rendered  latent. 

518.  Definition  of  Latent  Heat.— I7ie  latent 
heat  of  a  substance  is  the  quantity  of  heat  that  is 


LATENT  AND   SPECIFIC  HEAT.  331 

lost  to  thermometric  measurement  during  its  lique- 
faction or  vaporization,  or  the  amount  of  heat  that 
must  be  communicated  to  a  body  to  change  its 
condition  without  changing  its  temperature.  It  may 
be  made  to  reappear  during  the  opposite  changes  after  any 
interval  of  time.  Many  solids  may  undergo  two  changes 
of  condition.  Such  solids  have  a  latent  heat  of  liquefac- 
tion and  a  latent  heat  of  vaporization. 

519.  Latent  Heat  of  Fusion. — We  are  already 
familiar  with  the  fact  that  when  ice  or  any  other  solid  is 
melted  by  the  direct  application  of  heat,  much  of  the  heat 
is  rendered  latent.     In  the  case  of  melting  ice  we  shall 
show  how  this  latent  heat  is  measured,  and  that  its  quan- 
tity is  very  great.    We  may  represent  the  process  of  lique- 
faction of  ice  as  follows  : 

Water  at  0°  C.  —  ice  at  0°  C.  +  latent  heat  of  water. 

520.  Latent   Heat  of  Solution.— During  the 

process  of  solution,  as  well  as  during  fusion,  heat  is  ren- 
.dered  latent.  In  either  case  the  performance  of  the  icork 
of  liquefaction  demands  an  expenditure  of  kinetic  energy. 
Hence  the  solution  of  a  solid  involves  a  diminution 
of  temperature. 

(a.)  This  loss  may  in  some  cases  be  made  good  by  an  equal  in- 
crease, or  changed  to  gain  by  a  greater  increase  of  sensible  heat 
from  the  chemical  changes  involved  ;  but  in  any  case,  the  act  of 
liquefaction  considered  by  itself  produces  cold.  Thus  a  cup  of 
coffee  is  cooled  by  sweetening  it  with  sugar,  and  a  plate  of  soup  is 
cooled  by  flavoring  it  with  salt. 

521.  Freezing  Mixtures. — Ttic  latent  heat  of 
solution  lies  at  the   foundation  of  the  action  of 
freezing  mixtures.    For  example,  when  ice  is  melted 
by  salt,  and  the  water  thus  formed,  in  turn,  dissolves  the 


332  LATENT  AND  SPECIFIC  HEAT. 

salt  itself,  the  double  liquefaction  requires  a  deal  of  heat 
which  is  generally  furnished  by  the  cream  in  the  freezer. 
The  freezing  mixture  most  commonly  used  consists  of  one 
weight  of  salt  and  two  weights  of  snow  or  pounded  ice. 
The  mixture  assumes  a  temperature  of  —18°  C.,  which 
furnished  the  zero  adopted  by  Fahrenheit. 

(a.)  By  mixing,  at  the  free/ing  temperature,  three  weights  of 
snow  with  two  weights  of  dilute  sulphuric  acid,  the  temperature 
may  be  reduced  to  about  —20°  F.,  a  diminution  of  over  50  Fahren- 
heit degrees.  If  equal  weights  of  snow  and  dilute  sulphuric  acid 
be  thus  reduced  to  a  temperature  of—  20°  F.  and  then  mixed,  the 
temperature  will  fall  to  about— 60°  F.  By  mixing  equal  weights 
of  sodium  sulphate  crystals  (Glauber's  salt),  ammonium  nitrate  and 
water,  all  at  the  ordinary  temperature,  and  stirring  the  mixture 
with  a  thermometer,  the  temperature  will  be  seen  to  fall  from  about 
65°  F.  to  about  10°  F.,  which  is  considerably  below  the  freezing  point 
of  pure  water.  Glauber's  salt  and  chlorhydric  (muriatic)  acid  form 
a  good  freezing  mixture. 

522.  Solidification. — Solidification    signifies   the 
passage  from  the  liquid  to  the  solid  condition.    During 
solidification  there  is  an  increase  of  temperature. 
This  may  seem  paradoxical  in  certain  cases,  but,  even  in 
the  case  of  water,  it  is  true  that  solidification  is  a  warming 
process. 

(a.)  The  sensible  heat  that  disappeared  as  latent  heat  during 
liquefaction,  being  no  longer  employed  in  doing  the  work  of  main- 
taining liquidity,  is  reconverted  into  sensible  heat  and  immediately 
employed  in  increasing  the  molecular  vibrations.  The  molecular 
potential  energy  is  transmuted  into  molecular  kinetic  energy.  This 
is  frequently  illustrated  by  the  precaution  taken  in  winter  to  place 
tubs  of  water  in  vegetable  cellars  that  the  latent  heat  of  the  freez- 
ing water  may  be  changed  into  sensible  heat  and  thus  protect  the 
vegetables. 

523.  Temperature   of  Solidification.  —  The 

melting  point  is  the  highest  temperature  at  which  solidi- 


LATENT  AND  SPECIFIC  HEAT.  333 

fication  can  take  place,  but  it  is  possible  to  keep  substances 
in  the  liquid  condition  at  lower  temperatures.  "Water 
standing  perfectly  quiet  sometimes  cools  several  degrees 
below  the  melting  point  without  freezing,  but,  upon  agita- 
tion in  any  perceptible  degree,  solidification  immediately 
takes  place. 

(a.)  Persons  who  sleep  in  cold  chambers  sometimes  notice,  upon 
arising,  that  as  soon  as  they  touch  a  pitcher  of  water  that  has  been 
standing  in  the  room  over  night,  the  water  quickly  freezes.  If  a 
particle  of  ice  be  dropped  into  the  water  the  same  result  follows. 
We  may  say  that,  in  this  condition,  liquids  have  a  tendency  to  freeze 
which  is  kept  in  check  only  by  the  difficulty  of  making  a  beginning. 

524.  Heat  from  Solidification.— (1.)  By  surrounding, 
with  a  freezing  mixture,  a  small  glass  vessel  containing  water,  and 
a  mercury  thermometer,  the  temperature  of  the  water  may  be  re- 
duced to — 10°  C.  or — 12°  C.  without  freezing  the  water.  A  slight 
movement  of  the  thermometer  in  the  water  starts  the  freezing  and 
the  temperature  quickly  rises  to  0°  C. 

(2.)  Place  a  thermometer  in  a  glass  vessel  containing  water  at 
30°  C.  and  a  second  thermometer  in  a  large  bath  of  mercury  at  —10°  C. 
Immerse  the  glass  vessel  in  the  mercury.  The  temperature  of  the 
water  will  gradually  fall  to  0°C.,  when  the  water  will  begin  to 
freeze  and  its  temperature  become  constant.  In  the  meantime  the 
temperature  of  the  mercury  bath  rises,  and  continues  to  do  so  icliile 
the  water  is  freezing. 

(3.)  Dissolve  two  weights  of  Glauber's  salt  in  one  weight  of  hot 
water,  cover  the  solution  with  a  thin  layer  of  oil  and  allow  to  cool, 
in  perfect  quiet,  to  the  temperature  of  the  room.  By  plunging  a 
thermometer  into  the  still  liquid  substance,  solidification  (crystal- 
lization) is  started  and  the  temperature  rapidly  rises.  Dr.  Arnott 
found  that  this  experiment  was  successful  after  keeping  the  solu- 
tion in  the  liquid  condition  for  five  years. 

(4.)  Mix  equal  quantities  of  dilute  sulphuric  acid  and  of  a  satu- 
rated solution  of  calcium  chloride  (not  chloride  of  lime),  the  two 
liquids  having  been  allowed  time  to  acquire  the  temperature  of  the 
room.  The  two  liquids  are  converted  into  solid  calcium  sulphate, 
with  a  marked  increase  of  temperature.  In  this  case,  as  in  some 
of  the  other  cases,  part  of  the  heat  observed  is  probably  due  to 
chemical  action,  but  more  to  the  conversion  of  the  latent  heat  of 
the  liquids. 


334  LATENT  AND   SPECIFIC  HEAT. 

(5.)  To  three  weights  of  quicklime  add  one  weight  of  water. 
The  water  will  be  completely  solidified  in  the  slaking  of  the  lime 
with  remarkable  thermal  manifestations.  Carts  containing  quick- 
lime have  been  set  on  fire  by  exposure  to  heavy  rains. 

525.  Change  of  Bulk  during  Solidification. 

— Most  substances  shrink  in  size  during  solidification ;  but 
a  few,  such  as  ice,  cast-iron,  antimony  and  bismuth,  are 
exceptions.  When  melted  cast-iron  is  poured  into  a  mould, 
it  expands  in  cooling  and  presses  into  every  part  of  the 
mould.  The  tracings  on  the  casting  are,  therefore,  as  clear 
cut  as  they  were  in  the  mould.  A  clear-cut  casting  can 
not  be  obtained  from  lead ;  this  is  one  of  the  reasons  why 
antimony  is  made  a  constituent  of  type-metal.  Gold  coins 
have  to  be  stamped ;  they  cannot  be  cast  so  as  to  produce 
a  clear-cut  design.  The  bursting  of  pipes  by  freezing  water 
is  a  common  source  of  annoyance. 

(«.)  An  army  officer  at  Quebec  performed  the  following  experi- 
&  ment :    He  filled  a  12-inch 

shell  with  water  and  closed 
the  opening  with  a  wooden 
plug  forcibly  driven  in.  The 
shell  was  put  out  of  doors  ; 
the  temperature  being 
—28°  C.,  the  water  froze,  the 
plug  was  thrown  about  300 
feet,  and  a  tongue  of  ice 
about  eight  inches  long  pro- 
truded from  the  opening. 
In  a  similar  experiment,  the 
shell  split  and  a  rim  of  ice 
FIG.  253.  issued  from  the  rent. 

526.  Latent   Heat   of    Vaporization.  —  The 

vaporization  of  a  liquid  is  accompanied  by  the  disappear- 
ance of  a  large  quantity  of  heat,  and  frequently  by  a  diminu- 
tion of  temperature.  There  is  a  change  of  sensible  into 


LATENT  AND   SPECIFIC  HEAT. 


335 


FIG.  254. 

Crystals  of  ice 


latent  heat;  of  kinetic  into  potential  energy.  We  may 
represent,  for  instance,  the  va- 
porization of  water  as  follows  : 
Steam  at  100°  C.  =  water 
at  100°  C.  +  latent  heat  of 
steam. 

(a.)  The  cryophorus,  shown  in 
Fig.  254,  consists  of  a  bent  tube 
and  two  bulbs  containing  a  small 
quantity  of  water.  The  air  is  re- 
moved by  briskly  boiling  the  water. 
The  tube  is  sealed  while  the  steam 
is  escaping.  The  instrument  thus 
contains  only  water  and  aqueous 
vapor.  When  the  liquid  is  poured 
into  B,  and  A  is  placed  in  a  freez- 
ing mixture,  the  vapor  is  largely 
condensed  in  A  while  more  is  rapidly  formed  in  B. 
soon  form  on  the  surface  of  the  water  in  B. 

(b.)  Wet  a  block  of  wood  and  place  a  watch  crystal  upon  it.  A 
film  of  water  may  be  seen  under  the  central  part  of  the  glass.  Half 
fill  the  crystal  with  sulphuric  ether  and  rapidly  evaporate  it  by 
blowing  over  its  surface  a  stream  of  air  from  a  small  bellows.  So 
much  heat  is  rendered  latent  in  the  vaporization  that  the  watch 
crystal  is  firmly  frozen  to  the  wooden  block. 

527.  Condensation  of  Gases.— Gases  may  be 
condensed  by  union  with  some  liquid  or  solid,  by  cold  or 
by  pressure.  It  has  been  recently  shown  that  any  known 
gas  may  be  liquefied  by  cold  and  pressure.  In  any  case, 
the  condensation  of  a  gas  renders  sensible  a  large 
amount  of  heat. 

(a.}  Sulphurous  oxide  (S02)  previously  dried,  is  easily  liquefied 
by  passing  it  through  a  U-tube  immersed  in  a  freezing  mixture. 
When  some  of  this  liquid  is  placed  upon  mercury  in  a  small  capsule 
and  rapidly  evaporated  by  blowing  over  it  a  stream  of  air  from  a 
bellows,  the  mercury  is  frozen  (§497). 


336 


LATENT  AND  SPECIFIC  HEAT. 


FIG.  255. 


(&.)  The  change  of  latent  heat  into  sensible  during  the  condensa 
tion  of  a  gas  is  easily  illustrated 
by  the  following  experiment : 
Into  a  gas  bottle,  A,  put  a  tea- 
cup full  of  small  pieces  of  mar- 
ble, and  pour  in  enough  water  to 
cover  them  and  to  seal  the  lower 
end  of  the  thistle  tube.  From 
the  gas  bottle  lead  a  delivery 
tube  to  the  lower  part  of  a  bot- 
tle, B,  containing  a  thermome- 
ter, t.  From  this  bottle  lead  a 
tube  to  the  lower  part  of  the 
bottle  C,  which  contains  a  ther- 
mometer, T,  with  its  lower  part  embedded  in  a  teacup  full  of  salts 
of  tartar.  Through  the  thistle  tube  of  A  pour  muriatic  acid,  about  a 
thimble-full  at  a  time.  Carbonic  acid  gas  will  be  liberated  and  pass 
through  B  into  (7.  There  it  unites  with  the  potassium  carbonate, 
changing  it  to  potassium  bi-carbonate.  In  this  change  from  the 
aeriform  to  the  solid  condition,  the  carbonic  acid  gives  up  all  its 
latent  heat,  as  is  shown  by  the  remarkable  rise  of  the  thermometer 
in  C.  That  this  increase  of  temperature  is  not  due  to  the  sensible 
heat  of  a  hot  gas  is  shown  by  the  fact  that  t  is  scarcely  affected 
during  the  experiment. 

(c.)  When  the  vapor  is  condensed  to  the  liquid  or  solid  form,  the 
heat  previously  rendered  latent  is  given  out  as  sensible  heat ;  that 
is,  the  energy  of  position  is  changed  back  to  energy  of  motion.  In 
coming  together  again,  the  particles  yield  the  same  amount  of 
kinetic  energy  as  was  consumed  in  their  separation. 

528.  The  Latent  Heat  of  Water.— If  1  Ib.  of 

water  at  0°  C.  be  mixed  with  1  Ib.  of  water  at  80°  C.,  we 
shall  have  two  pounds  of  water  at  40°  C.  But  if  1  Ib.  of 
ice  at  0°  C.  be  mixed  with  1  Ib.  of  water  at  80°  C.,  we  shall 
have  two  pounds  of  water  at  0°  C.  The  heat  which  might 
be  used  to  warm  the  water  from  0°  to  80°  C.,  has  been  used 
in  melting  a  like  weight  of  ice.  Hence,  by  our  definition, 
we  see  that  the  latent  heat  of  water  is  80°  C.  (or  144°  F.) 
This  means  that  the  amount  of  heat  required  to  melt 
a  quantify  of  ice  without  changing  its  tempera- 


LATENT  AND  SPECIFIC  HEAT.  337 

ture  is  eighty  times  as  great  as  the  heat  required 
to  warm  the  same  quantity  of  water  one  centi- 
grade degree. 

(a.)  Because  of  this  great  latent  heat  of  water,  the  processes  of 
melting  ice  and  freezing  water  are  necessarily  slow.  Otherwise,  the 
waters  of  our  northern  lakes  might  freeze  to  the  bottom  in  a  single 
night,  while  "the  hut  of  the  Esquimaux  would  vanish  like  a  house 
in  a  pantomime,"  or  all  the  snows  of  winter  be  melted  in  a  single 
day  with  inundation  and  destruction. 

529.  The  Latent  Heat  of  Steam.— Experiment 
has  shown  that  the  amount  of  heat  necessary  to  evaporate 
one  pound  of  water  would  suffice  to  raise  the  temperature 
of  537  pounds  of  water  1°  C.    Hence  we  say  that  the  latent 
heat  of  steam  is  537°  C.  (or  967°  F.).    This  means  that  the 
amount  of  heat  required  to  evaporate  a  quantity 
of  water  without  changing  its  temperature  is  537 
times  as  great  as  the  heat  required  to  warm  the 
same  quantity  of  water  one  centigrade  degree. 

(a.)  When  a  pound  of  steam  is  condensed,  537  heat  units  (pound- 
centigrade)  are  liberated.  In  this  we  see  an  explanation  of  the 
familiar  fact  that  scalding  t>y  steam  is  so  painfully  severe.  Were 
it  not  for  the  latent  heat  of  steam,  when  water  reached  its  boiling 
point  it  would  instantly  flash  into  steam  with  tremendous  explosion. 

530.  Problems  and  Solutions. — (1.)  How  many  pounds 
of  ice  at  0°  C.  can  be  melted  by  1  pound  of  steam  at  100°  C.  ?    One 
pound  of  steam  at  100°  C.,  in  condensing  to  water  at  the  same  tem- 
perature, parts  with  all  its  latent  heat,  or  537  heat  units.     The 
pound  of  water  thus  formed  can  give  out  100  more  heat  units. 
Hence,  the  whole  number  of  heat  units  given  out  by  the  steam  in 
changing  to  water  at  0°  C.,  the  temperature  at  which  it  can  no  longer 
melt  ice,  is  537  +  100  =  637. 

Let  x  =  the  number  of  pounds  of  ice  that  can  be  melted.  Each 
pound  of  ice  melted  will  require  80  heat  units.  Hence,  80#  —  the 
number  of  heat  units  necessary.  The  heat  to  melt  the  ice  must 
come  from  the  steam. 

Therefore  80z  =  637.  /.  x  =  7.96  +  Ibs.    Ana. 

15 


338  LATENT  AND  SPECIFIC  HEAT. 

(2.)  How  many  pounds  of  steam  at  100°  C.  will  just  melt  100 
pounds  of  ice  at  0°  C.  ?  If  a;  represent  the  number  of  pounds  of 
steam  required,  that  quantity  of  steam  at  100°  C.  will  furnish  637# 
heat  units.  To  melt  100  Ibs.  of  ice,  (80  x  100  =)  8,000  heat  units 
will  be  required. 

Hence,  637z  =  8,000.  !  '*.   x  =  12.55  +  Ibs.     Am. 

(3.)  What  weight  of  steam  at  100°  C.  would  be  required  to  raise 
500  pounds  of  water  from  0°  C.  to  10°  C.  ? 

Let  x  =  the  number  of  pounds  of  steam  required. 

(537  +  90)z  =  500  x  10.  .-.  x  =  7.97  +  Ibs.    Ans. 

(4.)  If  4  Ibs.  of  steam  at  100  C.  be  mixed  with  200  Ibs.  of  water  at 
10°  C.,  what  will  be  the  temperature  of  the  water  ? 

Let  x  =  the  temperature.  In  condensing  to  water  at  100°  C.,  the 
4  Ibs.  of  steam  will  give  out  (537  x  4  =)  2,148  heat  units.  This 
4  Ibs.  of  water  will  then  give  out  4(100  —  x)  heat  units.  Hence,  the 
steam  will  impart  2,148  +  4(100  —  x)  heat  units.  The  200  Ibs.  of 
water  in  rising  from  10°  C.  to  x°  will  absorb  200(z  —  10)  heat  units. 

Hence,  2,148  +  4(100  -  x)  =  200(z  -  10).      .'. "  x  =  22.29°  C.    Ans. 

531.  Illustration  of  Specific  Heat.— When 
the  temperature  of  a  body  changes  from  30°  to  20°,  the 
body  loses  just  as  much  heat  as  it  gained  in  passing  from 
20°  to  30°.  This  heat  lost  by  a  cooling  body  may  be 
measured,  like  any  other  energy,  by  the  work  it  can  per- 
form. If  equal  weights  of  different  bodies  be  raised  to  the 
same  temperature,  the  amount  of  ice  that  each  can  melt 
will  be  proportional  to  the  number  of  thermal  units  they 
severally  contain.  A  pound  of  sulphur  at  212°  F.  will 
melt  £  as  much  ice  as  a  pound  of  boiling  water.  Hence, 
it  required  only  |  as  much  heat  to  heat  the  sulphur  from 
the  freezing  point  to  212°  F.,  as  it  did  to  heat  the  water 
to  the  same  temperature;  in  scientific  phraseology,  the 
specific  heat  of  sulphur  is  £. 

(a.)  In  an  experiment  of  this  kind,  if  the  cooling  substance  change 
Its  condition,  the  latent  heat  set  free  as  sensible  heat  must  be  taken 
Into  account.  Special  precaution  must  also  be  taken  in  measuring 


LATENT  AND  SPECIFIC  HEAT. 


339 


FIG.  256. 


the    heat    expended,   to    avoid   melting  of   the   ice   by   the  heat 

of  the  surrounding  air  and  making  proper 

allowance  for  the  heat  expended  in  warming 

the  apparatus  itself.     Fig.  256  represents  a 

form  of  calorimeter  frequently  used  in  such 

experiments.     M  contains  the  heated  body 

whose  weight  and  temperature  are  known. 

A  contains  the  ice  to  be  melted,  the  liquid 

thus  produced  escaping  by  D.     B  is  an  ice 

jacket  to  prevent  melting  of  the  ice  in  A  by 

the  heat  of  the  air. 

532.  Definition  of  Specific 
Heat. — TJie  specific  heat  of  a  body 
is  the  ratio  between  the  quantity 

of  heat  required  to  warm  that  body  one  degree  and 
the  quantity  of  heat  required  to  warm  an  equal 
iveight  of  water  one  degree. 

(a.)  It  is  very  important  to  bear  in  mind  that  specific  heat,  like 
specific  gravity,  is  a  ratio  ;  nothing  more  nor  less.  The  specific  heat 
of  water,  the  standard,  is  unity.  This  ratio  will  be  the  same  for 
any  given  substance,  whatever  the  thermal  unit  or  thermometric 
scale  adopted. 

533.  Specific  Heat  Determined  by  Mixture. 

— One  of  the  simplest  methods  of  measuring  specific  heat 
is  by  mixture.  Suppose,  e.  g.,  that  3  kilograms  of  mercury 
at  100°  C.  are  mixed  with  1  kilogram  of  ice-cold  water  and 
that  the  temperature  of  the  mixture  is  9°  C.  How  shall 
we  find  the  specific  heat  of  mercury  ? 

Let  x  —  the  specific  heat  of  the  mercury,  or  the  amount  of  heat 
lost  by  one  kilogram  of  mercury  for  each  degree  of  change  of 
temperature.  Then  will 

3.C  =  the  number  of  heat  units  lost  by  the  given  amount  of  mer- 
cury for  every  degree  of  change  of  temperature,  and  91  times 
3x,  or 

273ar  =  the  number  of  heat  units  lost  by  the  mercury  in  passing 
from  100°  to  9°  C. 

The  specific  heat  of  water  is  1.  This  multiplied  by  the  number 
of  kilograms  of  water  taken  is  1,  which  represents  the  number  of 


3dO 


LATENT  AND  SPECIFIC  HEAT. 


heat  units  gained  by  that  quantity  of  water  for  each  degree  of 
change  of  temperature.  Then  will  9  represent  the  number  of  heat 
units  gained  by  the  water  in  passing  from  0°  to  9°.  But  no  heat 
has  been  destroyed  or  wasted  ;  what  the  mercury  has  lost,  the  water 
has  gained. 

Mercury.  Water. 

Specific  heat x  1 

Weights  taken 3  1 

No.  of  degrees  of  change 91  9 

Heat  units .273z    =    9 

/.    x  =  .033,  the  specific  heat  of  mercury. 

534.  Heated  Balls  Melting  Wax.— The  differ- 
ence between  bodies  in  respect  to  specific  heat  may  be 
roughly  illustrated  as  follows :  small  balls  of  equal  weight, 
made  severally  of  iron,  copper,  tin,  lead  and  bismuth  are 
heated  to  a  temperature  of  180°  or  200°  C.  by  immersing 
them  in  hot  oil  until  they  all  acquire  the  temperature  of 
the  oil.    They  are  then  placed  on  a  cake  of  beeswax  about 

half  an  inch 
thick.  The  iron 
and  copper  will 
melt  their  way 
through  the 
wax,  the  tin  will 
nearly  do  so, 

while   the    lead 
FIG.  257.  -II-  .  i_ 

and    bismuth 

sink  not  more  than  half  way  through  the  wax. 

535.  Reference  Tables.— (1.)  Specific  Heat  of  some  sub- 
stances : 

Iron 1138 

Copper 0952 

Silver 0570 

Tin 0562 

Mercury 0333 

Lead..  .......     .0314 


Hydrogen 3.4090 

Water 1.0000 

Ajnmonia  (gas) 5084 

Air 2375 

Oxygen 2175 

Sulphur 2026 

Diamond 1469 


Bismuth 0308 


LATENT  AND  SPECIFIC  HEAT.  341 

(2.)  Specific  heat  of  some  substances  in  different  states  : 

Solid.  Liquid.  Aeriform. 

Water 5050  1.0000                .4805 

Bromine 0843  .1060                .0555 

Alcohol .5050                .4534 

Ether .5467                .4797 

536.  Specific  Heat  of  Water.—  Water  in  its 
liquid  form  has  a  higher  specific  heat  than  any 
other  substance  except  hydrogen.  For  this  reason  the 
ocean  and  our  lakes  are  cooled  and  heated  more  slowly 
than  the  land  and  atmosphere.  They  thus  modify  sudden 
changes  of  temperature,  and  give  rise  to  the  well  known 
fact  that  the  climate  of  the  sea-coast  is  warmer  in  winter 
and  cooler  in  summer  than  that  of  inland  places  of  the 
same  latitude.  The  heat  of  summer  is  stored  up  in  the 
ocean  and  slowly  given  out  during  the  winter.  This  fact 
also  explains  a  phenomenon  familiar  to  those  living  on  the 
borders  of  the  ocean  or  great  lakes.  Because  of  its  lower 
specific  heat,  the  land  becomes  during  the  day  more  heated 
than  the  water.  The  air  in  contact  with  the  land  thus 
becomes  more  heated,  expands,  rises  and  forms  an  upper 
current  from  the  land  accompanied  by  a  corresponding 
under  current  to  the  land,  the  latter  constituting  the 
welcome  sea  or  lake  breezes  of  summer.  After  sunset, 
however,  the  land  cools  more  rapidly  than  the  water,  the 
process  is  reversed,  and  we  have  an  under  current  from 
the  land  constituting  the  land  breeze. 

EXERCISES. 

1.  One  kilogram  of  water  at  40°  C.,  2  kilograms  at  30*  C.,  3  kilo- 
grams at  20°  C.,  and  4  kilograms  at  10°  C.  are  mixed.     Find  the  tem- 
perature of  the  mixture. 

2.  One  pound  of  mercury  at  20°  C.  was  mixed  with  one  pound  of 


343  LATENT  AND  SPECIFIC  HEAT. 

water  at  0°C.,  and  the  temperature  of  the  mixture  was  0.634°C. 
Calculate  the  specific  heat  of  mercury. 

3.  What  weight  of  water  at  85°  C.  will  just  melt  15  pounds  of 
iceatO°C.? 

4.  What  weight  of  water  at  95°  C.  will  just  melt  10  pounds  of  ice 
at  -10° C.? 

5.  What  weight  of  steam  at  125'  C.  will  melt  5  pounds  of  ice  at 
—8°  C.  and  warm  the  water  to  25°  C.  ? 

6.  How  much  mercury  could  be  wanned  from  10°  C.  to  20°  C.  by 
1  kilogram  of  steam  at  200°  C.  ? 

7.  Equal  masses  of  ice  at  0°  C.  and  hot  water  are  mixed.     The  ice 
is  melted  and  the  temperature  of  the  mixture  is  0°  C.     What  was 
the  temperature  of  the  water  ? 

8.  Ice  at  0°  C.  is  mixed  with  ten  tunes  its  weight  of  water  at 
20°  C.     Find  the  temperature  of  the  mixture.     Ans.  11°  C.  nearly. 

9.  One  pound  of  ice  at  0°  C.  is  placed  in  5  pounds  of  water  at 
12°  C.     What  will  be  the  result  ? 

10.  Find  the  temperature  obtained  by  condensing  10  g.  of  steam 
at  100°  C.  in  1  Kg.  of  water  at  0°  C. 

11.  A  gram  of  steam  at  100°  C.  is  condensed  in  10  grams  of  water 
»t  0°  C.     Find  the  resulting  temperature.  Ans.  58°  C.  nearly. 

12.  If  200  #.  of  iron  at  300°  C.  be  plunged  into  1  Eg.  of  water  at 
0°C.,  what  will  be  the  resulting  temperature  ? 

13.  Find  the  specific  heat  of  a  substance,  80  g.  of  which  at  100°  C. 
being  immersed  in  200  g.  of  water  at  10°  gives  a  temperature  of 
20°  C. 

14.  If  800 #.  of  copper  at  100°  C.  be  immersed  in  TOO/;,  of  alcohol 
at  0°  C.,  what  will  be  the  resulting  temperature  ?    (§  535.) 

15.  What  will  be  the  result  of  mixing  5  ounces  of  snow  at  0°  C. 
with  23  ounces  of  water  at  20°  C.  ? 

16.  A  pound  of  wet  snow  mixed  with  5  pounds  of  water  at  20°  C. 
yields  6  pounds  of  water  at  10°  C.    Find  the  proportions  of  snow 
and  water  in  the  wet  snow. 

17.  What  weight  of  mercury  at  0°  C.  will  be  raised  one  degree 
by  dropping  into  it  150  g.  of  lead  at  400°  C.  ? 

18.  Find  the  result  of  mixing  6  pounds  of  snow  r*t  0°  C.  with 
7  pounds  of  water  at  50°  C. 

Recapitulation. — In  this  section  we  have  considered 
the  definition  of  Thermal  Units;  two  Varieties 
of  Molecular  Energy  ;  their  mutual  Converti- 
bility ;  the  definition  of  Latent  Heat;  the  latent 


MODES    OF  DIFFUSING   HEAT.  343 

heat  of  Fusion  and  of  Solution ;  Freezing  Mix- 
tures ;  Solidification,  and  the  Temperature  of 
Solidification ;  Heat  from  Solidification ; 
Change  of  Bulk  during  solidifying;  the  Latent 
Heat  of  Vaporization  ;  the  Condensation  of 
Gases ;  the  Latent  Heat  of  Water  and  of 
Steam;  illustration  and  definition  of  Specific  Heat; 
specific  heat  Determined  by  Mixture;  specific 
heat  Determined  by  Melting  Wax;  tables  of 
specific  heat,  and  the  Specific  Heat  of  \Vater. 


ECTfON    IV, 


MODES    OF    DIFFUSING    HEAT. 

537.  Diffusion  of  Heat.— Heat  is  diffused  in  three  ways: 
by  conduction,  convection,  and  radiation.     Whatever  the  mode  of 
diffusion,  there  is  a  tendency  to  produce  uniformity  of  temperature. 

538.  Conduction. — If  one  end  of  an  iron  poker  be 
thrust  into  the 'fire,  the  other  end  will  soon  become  too 
warm  to  bo  handled.     It  has  been  heated  by  conduction, 
the  molecules  first  heated  giving  some  of  their  heat  to  those 
adjacent,  and  these  passing  it  on  to  those  beyond.     There 
was  a  transfer  of  motion  from  molecule  to  molecule.     TJie 
process  by  which  heat  thus  passes  from  the  hotter 
to  the  colder  parts  of  a  body  is  called  conduction 
of  heat.    The  propagation  is  very  gradual,  and  as  rapid 
through  a  crooked  as  through  a  straight  bar. 

539.  Differences  in  Conductivity.— If,  instead 
of  an  iron  poker,  we  use  a  glass  rod  or  wooden  stick,  the 
end  of  the  rod  may  be  melted  or  the  end  of  the  stick 


344 


MODES   OF  DIFFUSING   HEAT. 


FIG.  258. 

burned  without  rendering  the  other  end  uncomfortably 
warm.  We  thus  see  that  some  ^substances  are  good  con- 
ductors of  heat  while  some  are  not.  Thrust  a  silver  and 
a  German  silver  spoon  into  the  same  vessel  of  hot  water, 
and  the  handle  of  the  former  will  become  much  hotter 
than  that  of  the  latter. 

(a.)  Fig.  258  represents  a  bar  of  iron  and  one  of  copper  placed 
end  to  end  so  as  to  be  heated  equally  by  the  name  of  the  lamp. 
Small  balls  (or  nails)  are  fastened  by  wax  to  the  under  surfaces  of 
the  bars  at  equal  distances  apart.  More  balls  can  be  melted  from 
the  copper  than  from  the  iron.  The  number  of  balls  melted  off,  not 
the  rapidity  with  which  they  fall,  is  the  test  of  conductivity.  The 
rapidity  would  depend  more  upon  specific  heat. 

(&.)  Relative  thermal  conductivity  of  some  medals : 


Silver 100 

Copper 74 

Gold 53 

Brass 24 

Tin..  15 


Iron 12 

Lead 9 

Platinum 8 

German  silver 6 

Bismuth  .  2 


The  above-named  metals  arrange  themselves  in  the  same  order 
with  reference  to  the  conduction  of  electricity,  silver  being  the  best 
and  bismuth  the  poorest.  This  relation  suggests  a  similarity  of 
nature  between  these  two  "agents. 

54O.  Conductivity  of  Fluids.— Liquids  and 
aeriform  bodies  are  poor  conductors  of  heat.  The 
surface  of  a  liquid  may  be  intensely  heated  without  sensibly 
affecting  the  temperature  an  inch  below. 


MODES  OF  DIFFUSING  HEAT. 


345 


(a.)  Cork  the  neck  of  a  glass  funnel  and  pass  the  tube  of  an 
inverted  thermometer  through  the  cork,  or  use  an  air 
thermometer,  as  shown  in  the  figure.  Cover  the  ther- 
mometer bulb  to  the  depth  of  about  half  an  inch  with 
water.  Upon  the  water  pour  a  little  sulphuric  ether 
and  ignite  it.  The  heat  of  the  flame  will  be  intense 
enough  to  boil  a  small  quantity  of  water  held  over  it, 
but  the  thermometer  below  will  be  scarcely  affected. 
Fasten  a  piece  of  ice  at  the  bottom  of  a  glass  tube, 
and  cover  it  to  the  depth  of  several  inches  with  water. 
Hold  the  tube  at  an  angle  of  about  45°,  and  apply  the 
flame  of  a  lamp  below  the  upper  part  of  the  water. 
The  -water  there  may  be  made  to  boil  without  melting 
the  ice.  The  conductivity  of  gases  is  probably  lower 
FIG.  259.  than  that  of  liquids. 

541.  Convection. — Fluids  (with  the  exception  oi 
mercury,  which  is  a  metal)  being  poor  conductors,  they 
cannot  be  heated  as  solids  gen- 
erally are.  Water,  e.g.,  must  be 
heated  from  below;  the  heated 
molecules  expand  and  rise  while 
the  cooler  ones  descend  to  take 
their  place  at  the  source  of  heat. 
These  currents  in  heating  water 
may  be  made  visible  by  dropping 
a  small  quantity  of  cochineal  or 
oak  sawdust  into  the  vessel  con- 
taining the  water.  TJiis  method 
of  diffusing  heat,  "by  actual 
motion  of  heated  fluid  masses, 
is  called  convection.  Expansion 
by  heat  and  the  force  of  gravity  are  essential  to  convection. 
Since  aeriform  bodies  are  expanded  more  by  heat  than 
liquids  are,  these  currents  of  heated  gases  are  more  active 
than  those  of  liquids.  Hence  the  drafts  of  lamps  and 
stoves,  the  existence  of  trade  winds,  etc.  • 


FIG.  260. 


346  MODES  OF  DIFFUSING  HEAT. 

542.  The  Third  Mode  of  Heat  Diffusion.— When  a 

hand  is  held  over  a  heated  stove,  heat  is  carried  to  the  hand  by  con- 
vection and  given  up  to  the  hand  by  conduction.  But  when  the 
hand  is  held  before  the  stove  it  is  also  heated,  not  by  conduction,  for 
fluids  have  little  conducting  power  ;  not  by  convection,  for  convec- 
tion currents  are  ascending.  How  then  does  the  heat  get  to  the 
hand  ?  The  query  comes  to  us  with  still  greater  force  when  we 
consider  the  transmission  of  the  sun's  heat  to  the  earth,  for  the 
atmosphere  can  carry  it  by  neither  conduction  nor  convection. 
More  important  yet,  how  does  the  sun's  heat  reach  the  earth's 
atmosphere?  This  heat  passes  through  the  atmosphere  without 
heating  it.  If  along  a  poker  thrust  into  the  fire  the  hand  be  moved 
toward  the  stove,  the  temperature  increases.  If  a  person  ascend 
through  the  atmosphere  toward  the  sun  the  temperature  diminishes. 
We  have  here  a  wholly  new  set  of  thermal  phenomena,  heat  pass- 
ing through  a  substance  and  leaving  the  condition  of  that  substance 
unchanged. 

543.  Liiiminiferous  Ether. — In  the  case  of  actual, 
mechanical  energy,  the  rapid  motion  of  bodies,  e.  g.,  a 
vibrating  guitar  string,  is  partly  carried  off  by  the  air  in 
the  shape  of  sound.    When  the  sound  reaches  the  auditory 
nerve  it  represents  a  certain  amount  of  mechanical  energy 
of  motion  which  has  been  carried  from  the  string  by  the 
air.      ^ere  is  sufficient  reason  for  believing  that 
there  is  a  medium  pervading  all  space  which  car- 
ries off  part  of  the  invisible  motions  of  molecules, 
just  as  the  air  carries  off  a  portion  of  the  motion 
of  moving  masses.    This  medium,  called  the  luminiferous 
ether,  occupies  all  space.     The  gaps  between  the  sun,  the 
planets  and  their  satellites  are  filled  with  this  ether.     "  It 
makes  the  universe  a  whole  and  renders  possible  the  inter- 
communication of  light  and  energy  between  star  and  star." 

544.  Density  and  Elasticity  of  the  Ether.— This  ether 
is  wonderful,  not  only  in  its  incomprehensible  vastness  but  equally 
so  in  its  subtleness.     While  it  surrounds  the  suns  of  unnumbered 
systems  and  fills  all  interstellar  space,  it  also  surrounds  the  smallest 


MODES  OF  DIFFUSING   HEAT.  347 

particles  of  matter  and  fills  intermolecular  space  as  well.  It  is 
called  luminiferous  because  it  is  the  medium  by  which  light  is 
propagated,  it  serving  as  a  common  carrier  for  both  heat  and  light. 
We  have  seen  (§  426)  that  the  velocity  of  sound  depends  upon  two 
considerations,  the  elasticity  and  the  density  of  the  medium.  The 
enormous  velocity  with  which  the  ether  transmits  heat  and  light  as 
wave  motion  (about  186,000  miles  per  second),  compels  us  to  assume 
for  the  ether  both  extreme  elasticity  and  extreme  tenuity. 

545.  Radiant  Heat. — We  have  seen  that  the  mole- 
cules of  a  heated  hody  are  in  a  state  of  active  vibration. 
The  motion  of  these  vibrating  molecules  is  communicated 
to  the  ether  and  transmitted  by  it,  as  waves,  with  wonder- 
ful velocity.    Thus,  when  you  hold  your  hand  before  a  fire, 
the  warmth  that  you  feel  is  due  to  the  impact  of  these 
ether-waves  upon  your  skin  ;  they  throw  the  nerves  into 
motion,  just  as  sound-waves  excite  the  auditory  nerve,  and 
the  consciousness  corresponding  to  this  motion  is  what  we 
popularly  call  warmth.     Heat  thus  propagated  by  the 
ether,  instead  of  ~by  ordinary  forms  of  matter,  is 
Radiant  Heat.    TJie  process  of  propagation 

is  called  radiation.  t 

546.  The  Transmission  through  a 
Vacuum. — Iladiant  heat  will  traverse  a 
vacuum.    We  might  infer  this  from  the  fact 
that  the  sun  radiates  heat  to  the  earth.    It  may 
be  also  shown  experimentally. 

(a.)  A  thermometer  is  sealed  air-tight  in  the  bottom 
of  a  glass  globe  in  such  a  way  that  the  bulb  is  near  the 
centre  of  the  globe.     The  neck  of  the  flask  is  to  be     pIGi  26i. 
about  a  yard  long.     The  apparatus  being  filled  with 
mercury  and  inverted  over  a  mercury  bath,  a  Torricellian  vacuum 
is  formed  in  the  globe  and  upper  part  of  the  tube.     The  tube  is 
then  melted  off  above  the  mercury.    When  the  globe  is  immersed 
in  hot  water,  the  thermometer  immediately  indicates  a  rise  of  tern- 


348  MODES  OF  DIFFUSING  SEAT. 

perature.  There  is  no  chance  for  convection  ;  conduction  acts  much 
more  slowly. 

547.  Rectilinear  Propagation.— Radiant  heat 
travels    in    straight    lines    through    any    uniform 
medium. 

(a.)  Between  any  source  of  heat  and  a  thermometer  place  several 
•screens.  If  holes  be  made  in  the  screens  (See  Fig.  272)  so  that  a 
straight  line  from  the  source  of  heat  to  the  thermometer  may  pass 
through  them,  the  thermometer  will  be  affected  by  the  heat.  By 
moving  one  of  the  screens  so  that  its  opening  is  at  one  side  of  this 
line,  the  heat  is  excluded.  In  a  very  warm  day  a  person  may  step 
from  a  sunny  into  a  shady  place  for  the  same  reason.  The  heat  that 
moves  along  a  single  line  is  called  a  ray  of  heat. 

548.  Radiation  Equal  in  all  Directions.— 

Heat  is  radiated  equally  in  all  directions.  If  an 
iron  sphere  or  a  kettle  of  water  be  heated,  and  delicate 
thermometers  placed  on  different  sides  of  it  at  equal  dis- 
tances, they  will  all  indicate  the  same  temperature. 

549.  Radiation  Depends   upon    Tempera- 
ture  of  the   Source.— Tlie  intensity  of  radiant 
heat    is    proportional    to    the    temperature    of  the 
source. 

(a.)  Near  a  differential  thermometer,  place  a  vessel  of  water  10° 
warmer  than  the  temperature  of  the  room.  Notice  the  eifect  upon 
the  thermometer.  Heat  the  water  10°  more  and  repeat  the  experi- 
ment at  the  same  distance.  Then  heat  the  water  10°  still  more  and 
repeat  the  experiment  again.  The  effects  upon  the  thermometer  will 
be  as  the  numbers  one,  two  and  three. 

550.  Effect   of   Distance.— TJie   intensity  of 
radiant  heat  varies  inversely  as  the  square  of  the 
distance. 

(a.)  Place  the  differential  thermometer  at  a  certain  distance  from 
the  heated  water  and  note  the  effect.  Removing  the  thermometer 
to  twice  that  distance  the  effect  is  only  one-fourth  as  great,  etc. 


MODES   OF  DIFFUSING  HEAT.  349 

551.  Incident   Rays. — When    radiant    heat   falls 
upon  a  surface  it  maybe  transmitted,  absorbed  or  reflected. 
If  transmitted,  it  may  be  refracted.    Rock  salt  crystal 
transmits  nearly  all,  reflects  very  little,  and  absorbs  hardly 
any.     Lampblack  absorbs  nearly  all,  reflects  very  little,  and 
transmits  none.    Polished  silver  reflects  nearly  all,  absorbs 
a  little,  and  transmits  none. 

552.  Diathermancy. — Bodies  that  transmit  ra- 
diant heat  freely  are  called  diathermanous;  those 
that  do  not  are  called  athermanous.    These  terms 
are  to  heat,  what  transparent  and  opaque  are  to  light. 
Eock  salt  is  the  most  diathermanous  substance  known. 
Heat  that  is  radiated  from  a  non-luminous  source,  as  from 
a  ball  heated  below  redness,  is  called  obscure  heat ;  while 
part  of  that  radiated  from  a  luminous  source,  as  from  the 
sun  or  from  a  ball  heated  to  redness,  is  called  luminous 
heat.    Heat  from  a  luminous  source  is  generally  composed 
of  both  luminous  and  obscure  rays.     (§  652.) 

553.  Selective  Absorption. — The  power  of  any 
given  substance  to  transmit  heat  varies  with  the  nature  of 
the  heat  or  of  its  source.     For  example,  glass,  water  or 
alum  allows  the  sun's  luminous  heat  rays  to  pass,  while 
absorbing  nearly  all  of  the  heat  rays  from  a  vessel  filled 
with  boiling  water.    In  other  words,  these  substances  are 
diathermanous  for  luminous  rays,  but  athermanous  for 
obscure  rays.    The  physical  difference  between  luminous 
and  obscure  heat  rays  will  subsequently  be  explained. 

(a.)  A  solution  of  iodine  in  carbon  bi-sulphide  transmits  obscure 
rays  but  absorbs  luminous  rays.  By  means  of  these  substances, 
luminous  and  obscure  rays  may  be  sifted  or  separated  from  each 
other.  Dry  air  is  highly  diathermanous  ;  watery  vapor  is  highly 
athermanous  for  obscure  rays. 


350  REFLECTION  OF  HEAT. 

554.  Reflection  of  Heat.— When  radiant  heat 
falls  upon  an  athermanous  body,  part  of  it  is  generally 
absorbed  and  raises  the  temperature  of  the  body.  The 
rest  is  reflected,  the  energy  still  existing  in  the  ether  waves. 
The  angle  of  incidence  equals  the  angle  of  reflec- 
tion (§  97). 


FIG.  262. 

(a.)  In  Fig.  262,  the  source  of  heat  at  A  is  a  Leslie's  cube  filled  with 
hot  water.  S  is  an  athermanous  screen  with  an  aperture  for  the 
passage  of  rays  from  A  to  the  reflector  B.  The  line  CB  is  per- 
pendicular to  the  reflector.  When  D,  the  bulb  of  the  deferential 
thermometer,  is  placed  so  that  the  angle  ABC  equals  the  angle 
DBG,  the  reflected  rays  will  strike  the  bulb  and  raise  the  temper- 
ature. 

555.  Reflection  by  Concave  Mirrors.— By  the 

use  of  spherical  or  parabolic  mirrors,  remarkable  heating 
effects  may  be  produced.  When  parallel  rays  (like  the 
sun's  rays)  strike  directly  upon  such  a  mirror,  they  are 
reflected  to  a  focus.  Any  easily  combustible  substance 
held  at  the  focus  may  be  thus  ignited. 

(a.)  Two  such  mirrors  may  be  placed  as  shown  in  Fig.  263.  At 
the  focus  of  one  reflector  place  a  hot  iron  ball  ;  at  the  focus  of  the 
other,  a  bit  of  phosphorus  or  gun-cotton.  If  the  apparatus  be 
arranged  with  exactness,  the  combustible  will  be  quickly  ignited. 


REFRACTION  OF  HEAT. 


351 


FIG.  263. 

Replace  the  iron  ball  with  a  Leslie's  cube  containing  hot  water  ; 
at  the  focus  of  the  other  reflector  place  one  bulb  of  the  differential 
thermometer.  The  rise  of  temperature  at  this  focus  will  be  clearly 
shown,  even  irfien  the  oilier  bulb  is  nearer  the  source  of  heat  than  the 
focus  is. 

556.  Refraction  of  Heat.— When  rays  of  heat 
fall  obliquely  upon  a  diathermanous  body,  they  will  be 
bent  from  a  straight  line  on  entering  and  leaving  the  body. 
This  bending  of  the  ra,y  is  called  refraction.  Many 
rays  of  heat  may  thus  be  concentrated  at  a  focus,  as  in  the 
case  of  a  common  burning-glass.  By  the  aid  of  a  spectacle- 
glass,  the  sun's  rays  may  be  made  to  ignite  easily  combus- 
tible substances.  The  refraction  of  obscure  rays  cannot 
be  shown  by  a  glass  lens,  since  glass  is  athermanous  for 
such  rays.  But  if  a  rock-salt  lens  be  held  before  a  source 
of  obscure  heat,  and  the  face  of  a  thermopile  placed  at 


352  RADIANT  HEAT. 

the  focus  of  the  lens,  the  galvanometer  needle  will  at  once 
turn  aside,  showing  a  rise  of  temperature.  If  the  face  of 
the  pile  be  placed  anywhere  else  than  at  the  focus,  there 
will  be  no  such  deflection  of  the  needle. 

557.  Change  of  Radiant  into  Sensible  Heat. 

— Of  all  the  rays  falling  upon  any  substance,  only  those 
that  are  absorbed  are  of  effect  in  heating  the  body  upon 
which  they  fall.  The  motion  of  the  ether  waves  may  be 
changed  into  vibrations  of  molecules  of  ordinary  matter, 
and  thus  produce  sensible  heat,  but  the  same  energy  can- 
not exist  in  waves  of  ether  and  in  ordinary  molecular 
vibrations  at  the  same  time. 

(«.)  Phosphorus  or  gun-cotton  may  be  ignited  by  solar  rays  at 
the  focus  of  a  lens  made  of  clear  ice.  The  heat  rays  pass  through 
the  ice  without  melting  it.  It  is  only  when  the  radiation  is  stopped 
that  the  energy  of  the  ray  can  warm  anything. 

558.  Determination  of  Absorbing,  Reflecting  and 
Radiating    Powers.— For    experiments    in    determining   the 
absorbing,  reflecting  and  radiating  powers  of  solids,  the  apparatus 
generally  used  consists  of   a    Leslie's  cube,   concave  mirrors   of 
different  materials,  and  a  differential  thermometer  or  a  thermopile. 
The  Leslie's  cube  is  a  box  about  three  inches  on  each  edge,  the 
sides  being  made  of,  or  covered  with,  different  materials,  to  show 
their  differences  in  radiating  power.     The  cube  filled  with  hot  water 
is  placed  before  the  reflector,  and  a  bulb  of  the  thermometer  is 
placed  at  the  focus.     By  turning  different  faces  of  the  cube  toward 
the  mirror,  the  relative  radiating  powers  are  determined.    By  using 
different  mirrors,  the  reflecting  powers  are  determined.     By  coating 
the   bulb  with   different   substances,  their  absorbing  powers  are 
determined.      The   relative   radiating  powers   of  several  common 
substances  are  as  given  below : 


Lampblack 100 

Paper 98 

Crown  glass 90 


Tarnished  lead 45 

Mercury 20 

Gold,  silver,  copper 12 


559.  Mutual  Relations  of  Absorption,  Re- 
flection and  Radiation. — By  means  like  those  men- 


RADIANT  HEAT.  353 

tioned  in  the  last  paragraph,  it  has  been  shown  that 
good  absorbents  are  good  radiators  and  poor  re- 
flectors,  and  vice  versa ;  that  the  radiating  power  of  a 
body  depends  largely  upon  the  nature  of  its  surface  ;  that 
smoothing  and  polishing  the  surface  increases  reflecting 
power,  and  diminishes  absorbing  and  radiating  power; 
that  roughening  and  tarnishing  the  surface  increases  the 
absorbing  and  radiating  powers,  and  diminishes  the  re- 
flecting power.  Tlie  powers  of  absorption  and  radi- 
ation go  hand  in  hand.  (§§  654,  655.) 

(a.)  Make  a  thick  paint  of  a  teaspoonful  of  lampblack  and  a 
little  kerosene  oil.  With  this,  paint  the  right-hand  face  of  the 
left-hand  bulb  (tin  can  of  the  differential  thermometer  described  in 
Appendix  M).  Provide  another  oyster  can  and  paint  one  side  with 
the  lampblack.  Fill  this  third  can  with  boiling  water  and  place 
it  on  the  wooden  strips,  midway  between  the  two  tin  bulbs,  the 
two  blackened  surfaces  facing  each  other.  The  heat  radiated  and 
absorbed  by  the  two  blackened  surfaces  will  exceed  the  heat  radi- 
ated and  absorbed  by  the  two  equal  unpainted  surfaces  that  face 
each  other.  The  movement  of  the  colored  alcohol  in  the  tube  will 
show  this  to  be  true. 

56O.  Sympathetic  Vibrations.— The  relation 
between  radiation  and  absorption  of  heat  is  closely  analo- 
gous to  the  relation  between  the  radiation  and  absorption 
of  sound.  If  a  set  of  sound  waves  fall  upon  a  string 
capable  of  producing  similar  waves,  the  string  is  set  in 
motion  and  the  sound  waves  weakened  (§  443).  When 
ether  waves  of  a  given  kind  fall  upon  a  body  whose  mole- 
cules are  able  to  vibrate  at  the  same  rate,  and  thus  to 
reproduce  similar  waves,  the  kinetic  energy  is  transferred 
from  the  ether  to  the  molecules,  the  molecules  are  heated, 
the  radiant  energy  absorbed.  This  ability  to  absorb  wave 
motion  of  any  particular  kind,  implies  the  ability  to  repro- 
duce the  same  kind  of  waves.  It  therefore  is  easily  seen 


354  MODES  OF  DIFFUSING   HEAT. 

that  a  body  that  can  absorb  any  particular  kind 
of  heat  rays  can  radiate  the  same  kind. 

Note. — It  will  be  seen  further  on,  that  obscure  heat  rays  differ 
from  light  only  in  the  matter  of  wave  length.  Most  of  the  phenomena 
of  one  may  be  shown  to  pertain  to  the  other.  Absorption,  radiation, 
reflection,  transmission  and  refraction  of  rays  follow  the  same  laws, 
whether  the  agent  be  called  heat  or  light.  Other  phenomena,  such 
as  interference  and  polarization,  more  satisfactorily  studied  with 
luminous  rays,  have  been  produced  with  obscure  rays.  It  should 
be  borne  in  mind  that  the  most  delicate  instruments  yet  made  are 
far  less  sensitive  to  obscure  heat  than  is  the  eye  to  light.  A  candle 
flame  may  be  seen  a  mile  away  ;  any  one  might  well  be  pleased  with 
an  instrument  that  would  detect  its  heat  at  the  distance  of  a  rod. 

QUESTIONS. 

1.  Good  conductors  feel  warmer  or  cooler  to  the  touch  than  poor 
conductors  of  the  same  temperature.     Why  ? 

2.  Why  is  it  so  oppressively  warm  when  the  sun  shines  after  a 
Bummer  shower  ? 

3.  Why  is  there  greater  probability  of  frost  on  a  clear  than  on 
a  cloudy  night  ? 

4.  Can  a  good  absorbent  be  a  good  reflector  of  heat  ?    Is  a  good 
absorbent  a  good  radiator,  or  otherwise  ? 

5.  Explain  why  the  glass  covering  of  a  hot-bed  or  conservatory 
renders  the  confined  air  warmer  than  the  atmosphere  outside. 

6.  From  your  own  experience,  decide  which  is  the  better  con- 
ductor of  heat,  linen  or  woolen  goods,  oil  cloth  or  carpet. 

7.  Why  are  the  double  walls  of  ice-houses  filled  with  sawdust  ? 
Why  do  fire-proof  safes  have  double  walls  inclosing  plaster-of- 
Paris  or  alum  ? 

8.  Why  do  furnace  men,  firemen  and  harvesters  wear  woolen 
clothing  ?     Explain  the  use  of  double  windows. 

9.  How  may  heat  be  diffused  ?     How  is  the  surface  of  the  earth 
and  how  is  the  atmosphere  heated  ?     Can  you  boil  water  in  a  vessel 
with  heat  applied  from  above  ?    Why? 

Recapitulation. — In  this  section  we  have  considered 
Conduction;  the  conductivity  of  Fluids;  Con- 
vection; the  Luminiferous  Ether,  its  Den- 


THERMODYNAMICS.  355 

sity  and  Elasticity ;  Radiant  Heat,  and  Ra- 
diation;  Diathermancy;  Selective  Absorp- 
tion; Reflection  from  plane  and  concave  surfaces; 
Refraction  ;  the  Change  from  radiant  into  sensible 
heat;  the  determination  of  Absorbing,  Reflecting 
and  Radiating  Powers,  and  their  Mutual  Re- 
lations ;  Sympathetic  Vibrations.  ' 


V, 


THERMODYNAM  ICS. 

561.  Definition  of  Thermodynamics.—  Ther- 
modynamics is  the  branch  of  science  that  considers 
the  connection  between  heat  and  mechanical  work. 
It  has  especial  reference  to  the  numerical  relation  between 
the  quantity  of  heat  used  and  the  quantity  of  work  done. 

5O2.  Correlation  of  Heat  and  Mechanical  Energy. 

—  We  know  that  heat  is  not  a  form  of  matter  because  it  can  be 
created  in  any  desired  quantity.  We  must  continually  remember 
that  it  is  a  form  of  energy.  When  heat  is  produced  some  other 
kind  of  energy  must  be  destroyed.  Conversely,  when  heat  is  de- 
stroyed, some  other  form  of  energy  is  created.  Considered  as  heat 
merely,  this  agent  may  be  annihilated  ;  considered  as  energy,  it 
may  only  be  transformed.  The  most  important  transformations  of 
energy  are  those  between  heat  and  mechanical  energy.  The  process 
of  working  these  transformations  will  be  considered  directly.  It  is 
to  be  noticed,  however,  that  while  we  may  be  able  to  effect  a  total 
conversion  of  mechanical  energy  into  heat,  we  are  not  able  to  bring 
about  a  total  conversion  of  heat  into  mechanical  energy. 

563.  Heat  from  Percussion.  —  A  small  iron  rod 
placed  upon  an  anvil  may  be  heated  to  redness  by  repeated 
blows  of  a  hammer.  The  energy  of  ths  moving  mass  is 


356 


THKRMOD  YNAMICS. 


broken  up,  so  to  speak,  and  distributed  among  the  mole- 
cules, producing  that  form  of  molecular  motion  that  w%e  call 
heat.  The  same  transformation  was 
illustrated  in  the  kindling  of  a  fire  by 
the  "flint  and  steel "  of  a  century  ago. 
It  may  be  experimentally  illustrated 
by  the  "air-syringe." 

(a.)  The  air-syringe  consists  of  a  cylinder 
of  metal  or  glass  and  an  accurately  fitting 
piston.  By  suddenly  driving  in  the  piston, 
the  air  is  compressed  and  heat  developed. 
A  bit  of  gun  cotton  previously  placed  in 
the  cylinder  may  thus  be  ignited.  If  the 
cylinder  be  made  of  glass,  and  a  bit  of  ordi- 
nary cotton  dipped  in  sulphuric  ether  be 
used,  repeated  flashes  of  light  may  be  pro- 
duced by  successive  combustions  of  ether 
vapor.  The  fumes  of  one  combustion 
must  be  blown  away  before  the  next  com- 
bustion is  attempted. 

564.  Heat  from  Friction.— 

Common  matches  are  ignited  and  cold 
hands  warmed  by  the  heat  developed 
by  friction.  It  is  said  that  some  savages  kindle  fires 
by  skilfully  rubbing  together  well-chosen  pieces  of  wood. 
In  the  case  of  the  axles  of  railway  cars  and  ordinary  car- 
riages, this  conversion  of  mechanical  energy  into  heat  is 
not  so  difficult  as  its  prevention.  Lubricants  are  used  to 
diminish  the  friction  and  prevent  the  waste  of  energy  due 
to  the  undesirable  transformation.  A  railway  train  is 
really  stopped  by  the  conversion  of  its  motion  into  heat. 
When  this  has  to  be  done  quickly,  the  change  is  hastened 
by  increasing  the  friction  by  means  of  the  brakes.  Ex- 
amples of  this  change  are  matters  of  every  day  experience. 


FIG.  264. 


THERMOD  YNAMICS. 


357 


(a.}  Attach  a  brass  tube  10  cm.  long,  about  2  cm.  in  diameter  and 
closed  at  the  bottom,  to  a  whirling  table.  Partly  fill  the  tube  with 
cold  water  and  cork  the  open  end.  Press  the  tube  between  two 
pieces  of  board  hinged  together  as  shown  in  the  figure.  The  boards 


FIG.  265. 

should  have  two  grooves  for  the  reception  of  the  tube  ;  the  inner 
faces  of  the  boards  may  be  covered  with  leather.  When  the  machine 
is  set  in  motion  the  friction  warms  and  soon  boils  the  water.  The 
steam  drives  out  the  cork  with  explosive  violence. 

565.  First  Law  of  Thermodynamics.—  When 
heat   is    transformed    into   mechanical    energy   or 
mechanical  energy  into  heat,  the  quantity  of  heat 
equals  the   quantity  of  mechanical  energy.     This 
principle  is  the  corner-stone  of  thermodynamics.    It  is 
a  particular  case  under  the  more  general  law  of  the  Con- 
servation of  Energy. 

566.  Joule's  Equivalent. — It  is  a  matter  of  great 
importance  to  determine  the  numerical  relation  between 
heat  and  mechanical  energy ;  to  find  the  equivalent  of  a 
heat  unit  in  units  of  work.     This  equivalent  was  first 
ascertained  by  Dr.  Joule,  of  Manchester,  England.    His 


358  THERMODYNAMICS. 

experiments  were  equal  in  number  and  variety  to  the  im- 
portance of  the  subject.  He  showed  that  the  mechanical 
value  of  a  heat  unit  is  772  foot-pounds,  referring  to 
the  Fahrenheit  degree;  1390  foot-pounds  refer- 
ring to  the  centigrade  degree.  This  is  expressed  by 
saying  that  the  "mechanical  equivalent"  of  heat  is  772  or 
1390  foot-pounds.  (§  514  [>].) 

(a.)  A  change  in  the  unit  of  weight  will  not  affect  these  numbers, 
which  must  not  le  forgotten.  If  the  heat  unit  be  "  kilogram-Fahren- 
heit," the  equivalent  will  be  772  foot-kilograms  ;  if  the  thermal  unit 
be  "  gram-centigrade,"  the  equivalent  will  be  1390  foot-grams.  A 
change  in  the  unit  of  length  will  work  a  change  in  the  number 
representing  the  equivalent.  If  the  equivalent  for  a  "kilogram- 
centigrade  "  heat  unit  be  desired  in  kilogrammeters  instead  of  foot- 
kilograms,  the  number  1390  must  be  divided  by  the  ratio  between 
the  values  of  a  foot  and  a  meter,  becoming  thus  424.  kilogrammeters. 

567.    The  Use  of  Joule's  Equivalent.—  The 

use  of  the  mechanical  equivalent  of  heat  may  be  well  shown 
by  the  solution  of  a  problem. 

(a.)  If  a  cannon-ball  weighing  192.96  pounds  and  moving  with  a 
velocity  of  2000  feet  per  second,  be  suddenly  stopped  and  all  of  its 
kinetic  energy  converted  into  heat,  to  what  temperature  would  it 
warm  100  pounds  of  ice-cold  water  ? 

MB*       192.96x4000000      ^OAAAAAA  - 
Kinetic  energy  =  -—  =  -    —         ---  =  12000?00  foot-pounds. 


12000000  +•  772  =  15544  +  heat  units. 

15544  _j_  100  —  155.44  heat  units  for  each  pound  of  water.  This 
would  raise  the  temperature  155.44°  F.,  leaving  it  at  187.44°  F.  Ans. 

(&.)  Knowing  the  weight  of  the  earth  and  its  orbital  velocity,  we 
may  easily  compute  the  amount  of  heat  that  would  be  developed  by 
the  impact  of  the  earth  against  a  target  strong  enough  to  stop  its 
motion.  The  heat  thus  generated  from  the  kinetic  energy  of  the 
earth  would  be  sufficient  to  fuse  if  not  vaporize  it,  equalling 
that  derivable  from  the  combustion  of  fourteen  globes  of  coal 
each  equal  to  the  earth  in  size.  After  the  stoppage  of  its  orbital 
motion  it  would  surely  be  drawn  to  the  sun  with  continually 
increasing  velocity.  The  heat  instantaneously  developed  from 


THERMODYNAMICS.  359 

this  impact  of  the  planetary  projectile  would  equal  that  derivable 
from  the  combustion  of  5600  globes  of  coal  each  equal  to  the  earth 
in  size.  This  is  the  measure  of  the  potential  energy  of  the  earth 
considered  as  a  mass  separated  from  the  sun. 

568.  Chemical  Affinity.— We  have  already  seen 
that  there  are  forces  in  nature  compared  with  which  the 
force  of  gravity  is  insignificant.     (Read  carefully  the  first 
paragraph,  in  this  chapter.)     When  coal  is  burned,  the 
carbon  and  oxygen  particles  rush  together  with  tremendous 
violence,  energy  of  position  being  converted  into  energy  of 
motion.     The  molecular  motions  produced  by  this  clashing 
of  particles  constitute  heat  and  have  a  mechanical  value. 

569.  Heating  Powers. — If  a  pound  of  carbon  be 
burned,  the  heat  of  the  combustion  would  raise  about 
8000  pounds  of  water  1°  C.    In  like  manner,  the  combus- 
tion of  a  pound  of  hydrogen  would  yield  about  34000  heat 
units  (pound-centigrade). 

(a.)  The  following  table  shows  the  heating  powers  of  several 
substances  when  burned  in  oxygen : 


Hydrogen 34,462 

Marsh  gas  (CH4) 13,063 

Petroleum 12,300 

Carbon 8,080 


Alcohol  (C3 H60) 6,850 

Phosphorus 5,747 

Carbon  protoxide  (CO) 2,403 

Sulphur 2,220 


(ft.)  The  calorific  powers  mentioned  above  maybe  adapted  to  Fah- 
renheit degrees  by  multiplying  them  respectively  by  |.  As  they 
stand,  the  numbers  represent  the  number  of  times  its  own  weight 
of  water  that  could  be  warmed  1°C.  by  burning  the  substance  in 
oxygen. 

57O.  The  Steam -Engine. —The  steam-engine  is  a 
machine  for  utilizing  the  tension  of  steam.  Its  essential 
parts  are  a  boiler  for  the  generation  of  steam,  and  a  cylinder 
for  the  application  of  the  tension  to  a  piston. 


360  THE  STEAM-ENGINE. 

(a.)  As  in  the  case  of  water-power  the  production  of  mechanical 
kinetic  energy  involves  the  fall  of  water  from  a  higher  to  a  lower 
level,  so  in  the  case  of  steam-power  the  production  of  visible 
energy  involves  the  fall  of  heat  from  a  higher  to  a  lower  temper- 
ature. 

571.  Single- Acting   Engine. — In  a  single-acting  steam- 
engine,  the  piston  is  pushed  one  way  by  the  tension  of  the  steam. 
The  steam  is  then  condensed  and  the  piston  driven  back  by  atmos- 
pheric pressure.    Such  engines  have  gone  out  of  use  and  have  only 
an  historical  interest. 

572.  Double  -  Acting   Engine. — In  a  double- 
acting  steam-engine,  the  steam  is  admitted  to  the  cylinder 
alternately  above  and  below  the  piston.    This  alternate 
admission  of  the  steam  is  accomplished  by  means  of  a 
sliding-valve.    The  sliding- valve  is  placed  in  a  steam-chest,, 
89  which  is  fastened  to  the  side  of  the  cylinder  C. 


FIG.  266. 

(a.)  In  the  figure,  the  steam-chest  is  represented  as  being  placed 
at  a  distance  from  the  cylinder;  this  is  merely  for  the  purpose 
of  making  plain  the  communicating  passages  to  and  from  the 
chest.  Steam  from  the  boiler  enters  at  M,  passes  through  A  to  the 


THE  STEAM-ENGINE,  361 


FIG.  267. 

cylinder,  where  it  pushes  down  the  piston  as  indicated  by  the 
arrows.  The  steam  below  the  piston  escapes  by  B  and  N.  As  the 
piston  nears  the  opening  of  B  in  the  cylinder,  the  sliding- valve  is 
raised,  by  means  of  the  rod  R,  to  the  position  indicated  in  Fig. 
267.  Steam  now  enters  the  cylinder  by  B  and  pushes  up  the  piston. 
The  steam  above  the  piston  escapes  by  A  and  N".  As  the  piston 
nears  the  opening  of  A  in  the  cylinder,  the  sliding- valve  is  pushed 
down  by  R  and  the  process  is  thus  repeated.  The  piston-rod  and 
the  sliding- valve  rod  work  through  steam-tight  packing-boxes. 

573.  The  Eccentric. — By  means  of  a  crank  or 
similar  device,  illustrated  in  common  foot-power  machinery 
like  the  turning-lathe,  scroll-saw,  or  sewing-machine,  the 
alternating  rectilinear  motion  of  the  piston-rod  is  changed 
into  a  continuous  rotary  motion.  A  circular  shaft  is  thus 
given  a  revolution  for  every  to-and-fro  movement  of  the 
piston.  This  shaft  generally  carries  an  eccentric  for  work- 
ing the  sliding-valve  rod  R.  The  eccentric  (Fig.  268)  con- 
sists of  a  circular  piece  of  metal,  e,  rigidly  attached  to  the 
shaft  of  the  engine  S,  in  such  a  position  that  the  centre  of 
the  piece  does  not  coincide  with  the  centre  of  the  shaft, 
16 


362 


THE  STEAM-ENGINE. 


The  eccentric  turns  within  a  collar,  which  is  fastened  to 
the  frame  T.  Every  turn  of  the  shaft  moves  the  eccentric 
with  its  collar  and  the  frame  T,  backward  and  forward  into 
the  two  positions  indicated  by  the  full  and  dotted  lines  of 


FIG.  268. 


Fig.  268.  The  point  a  may  be  fastened  directly  to  the 
sliding-valve  rod  or  through  the  agency  of  the  bent  lever 
abc,  as  the  circumstances  of  the  case  render  more  desirable. 

574.    The    Governor   and   Fly- Wheel.— The 

admission  of  steam  through  M  (Fig.  267)  is  regulated  by  a 
throttle-valve  worked  by  a  governor  (Fig.  269).  A  vertical 
shaft  is  given  a  rotary  motion  by  the  machinery.  To  the 
top  of  this  rod  are  hinged  two  arms  carrying  heavy  balls,  lb. 
From  these  arms,  supports  extend  to  a 
collar,  c,  surrounding  the  vertical  rod. 
This  collar  is  connected  with  a  valve  con- 
trolling the  admission  of  steam  to  the 
valve-chest  in  such  a  way  that  when  the 
collar  rises  the  valve  closes.  As  the 
machinery  increases  its  speed,  the  balls 
revolve  more  rapidly  about  the  vertical 
axis  and  tend  to  fly  further  apart  (§  74). 
In  doing  so,  they  raise  the  collar  and  partly  close  the  valve, 
diminishing  the  supply  of  steam.  The  machinery  is  thus 
made  to  slacken  its  speed,  the  balls  fall,  and  the  valve  opens. 
The  rapidity  of  motion  can  therefore  be  confined  within 


FIG.  269. 


THE  STEAM-ENGINE.  363 

the  limits  due  to  closing  the  throttle-valve  and  throwing 
it  wide  open.  Further  than  this,  smoothness  of  motion  is 
secured  by  attaching  a  heavy  fly-wheel  to  the  shaft  of  the 
engine.  A  little  reflection  will  show  that  the  fly-wheel 
also  acts  as  an  accumulator  of  energy. 

575.  The  Safety- Valve. — The    safety-valve  is  a 
necessary  part  of  every   steam-boiler.     It  consists  of  a 
valve,  F,  held  down  over  an  opening  in  the  top  of  the 
boiler  by  means  of  a  spring  or  a 

loaded  lever  of  the  second  class. 

The  force  with  which  the  valve 

is  held  down  is  to  be  less  than 

the  strength  of  the  boiler,  i.  e., 

the  force  must  be  such  that  the  FIG.  270. 

valve  will  open  before  the  tension 

of  the  steam  becomes  dangerous.      On  steamboats,  the 

weight,  W,  is  generally  locked  in  position  by  a  Government 

officer. 

576.  Non- Condensing1    Engines. — When   the 
steam  is  forced  out  at  N  (Fig.  267),  it  has  to  overcome  an 
atmospheric  pressure  of  15  pounds  to  the  square  inch. 
This  must  be  deducted  from  the  total  tension  of  the  steam 
to  find  the  available  power  of  the  engine.     Such  an  engine 
is  known  as  a  non-condensing  engine.    It  may  be  recog- 
nized by  the  escape  of  steam  in  puffs.    It  is  generally  a 
high-pressure  engine.     The  railway  locomotive  is  a  high- 
pressure,  non-condensing  engine. 

577.  Condensing  Engines.— The  steam  may  be 
conducted  from  the  exhaust  pipe  N  (Fig.  267)  to  a  chamber 
called  a  condenser.     Steam  from  the  cylinder  and  a  jet  of 
cold  water  being  admitted  at  the  same  time,  a  vacuum  is 


364  THE  STEAM-ENGINE. 

formed  and  the  loss  of  energy  due  to  atmospheric  pressure 
is  avoided.  Such  an  engine  is  known  as  a  condensing,  or 
low-pressure  engine. 

(a.)  Low-pressure  engines  are  always  condensing  engines.  A  low- 
pressure  engine  will  do  more  work  with  a  given  amount  of  fuel 
than  a  high-pressure  non-condensing  engine  will,  is  less  liable  to 
explosion,  and  causes  less  wear  and  tear  to  the  machinery.  But  it 
must  be  larger,  more  complicated,  more  costly,  and  less  portable. 

578.  Heat  and  Work  of  Steam-Engines.— 

More  heat  is  carried  to  the  cylinder  of  a  steam-engine  than 
is  carried  from  it.  The  piston  does  work  at  every  stroke, 
and  this  work  comes  from  the  heat  that  disappears.  Every 
stroke  of  the  piston  annihilates  heat.  Careful  experiments 
show  that  the  heat  destroyed  and  the  work  performed  are 
in  strict  agreement  with  Joule's  equivalent.  With  a  given 
supply  of  fuel,  the  engine  will  give  out  less  heat  when  it 
is  made  to  work  hard  than  when  it  runs  without  doing 
much  work. 

EXERCISES. 

1.  The  mechanical  equivalent  of  heat  is  1390  foot-pounds.    What 
is  it  in  kilogrammeters  ? 

2.  Find  the  weight  of  water  that  may  be  warmed  15°  C.  by  burn- 
ing 1  ounce  of  sulphur  in  oxygen. 

3.  What  weight  of  water  would  be  heated  from  0°  C.  to  1°  C.  by 
the  combustion  of  one  gram  of  phosphorus  ? 

4.  One  gram  of  hydrogen  is  burned  in  oxygen.     To  what  tempera- 
ture would  a  kilogram  of  water  at  0°  C.  be  raised  by  the  combustion  ? 

5.  Prom  what  height  must  a  block  of  ice  at  0°  C.  fall  that  the  heat 
generated  by  its  collision  with  the  earth  shall  be  just  able  to  melt  it? 

6.  From  what  height  must  it  fall  that  the  heat  generated  may  be 
sufficient  to  vaporize  it  ? 

7.  To  what  height  could  a  ton  weight  be  raised  by  utilizing  all  the 
heat  produced  by  burning  5  Ibs.  of  pure  carbon  ? 

8.  Find  the  height  to  which  it  could  be  raised  if  the  coal  had  the 
following  percentage  composition : 

0  =  88.42;    H=  5.61 ;    0  =  5.97. 


THERMODYNAMICS.  365 

9.  To  what  temperature  would  a  cannon-ball  weighing  150  Ibs. 
and  moving  1920  feet  per  sec.,  warm  2000  Ibs.  of  water  at  32°  F.,  if 
its  motion  were  suddenly  converted  into  heat  ? 

10.  (a.)  How  many  pounds  of  water  can  be  evaporated  by  80  Ibs. 
of  pure  carbon  ?    (&.)  If  applied  to  iron,  how  many  pounds  could  b« 
heated  from  0°  F.  to  2000°  F.  1 

11.  With  what  velocity  must  a  10-ton  locomotive  move  to  give 
a  mechanical  energy  equivalent  to  the  heat  necessary  to  convert 
48  pounds  of  ice  at  0°  C.  to  steam  at  100°  C.  ? 

12.  An  8-lb.  ball  is  shot  vertically  upward  in  a  vacuum  with  a 
velocity  of  2000  feet.     How  many  pounds  of  water  may  be  raised 
from  the  freezing  to  the  boiling  point  by  the  heat  generated  when 
it  strikes  the  earth  on  its  descent  ? 

13.  (a.)  From  what  height  must  water  fall  in  order  to  raise  its 
own  temperature  1°  C.  by  the  destruction  of  the  velocity  acquired, 
supposing  no  other  body  to  receive  any  of  the  heat  thus  generated? 
(Answer  to  be  given  in  meters.)    (&.)  How  far  must  mercury  fall  to 
produce  the  same  effect  ?    (Specific  heat  of  mercury  =  ,0333.) 

14.  With  a  velocity  of  how  many  cm.  per  second  must  a  leaden 
bullet  strike  c,  target  that  its  temperature  may  be  raised  100°  C.  by 
the  collision,  supposing  all  the  energy  of  the  motion  to  be  spent  in 
heating  the  bullet  ?    (Specific  heat  of  lead =.031 4;  g. =980  cm.   %  127.) 

15.  A  steam-engine  raises  a  ton  weight  386  ft.     How  many  heat 
units  are  thus  expended  ? 

16.  A  64-pound  cannon-ball  strikes  a  target  with  a  velocity  of 
1400  feet  per  second.     Supposing  all  the  heat  generated  to  be  given 
to  60  pounds  of  water,  how  many  centigrade  degrees  would  the 
temperature  of  the  water  be  raised  ? 

17.  A  cannon-ball  weighing  7  pounds  strikes  an  iron  target  with  a 
velocity  of  1000  foet  per  second.     Suppose  the  whole  of  the  motion 
to  be  converted  into  heat  and  the  heat  uniformly  distributed  through 
70  pounds  of  the  target,  determine  the  change  of  temperature  thus 
produced.     (Specific  heat  of  iron  =  .1138.) 

18.  The  specific  heat  of  tin  is  .056  and  its  latent  heat  is  25.6  Fah- 
renheit degrees.     Find  the  mechanical  equivalent  of  the  amount  of 
heat  needed  to  heat  6  pounds  of  tin  from  374°  F.  to  its  melting  point 
442°  F.  and  to  melt  it. 

19.  A  lead  ball  strikes  a  target  with  a  velocity  of  1200  feet  per 
second.     Show  that  the  heat  generated  would  be  sufficient  to  fuse 
the  lead.     (See  §  497  and  §  535.     The  latent  heat  of  lead  is  5.4°  C.) 

20.  The  mechanical  equivalent  of  heat  is  772  foot-pounds,  refer- 
ence being  made  to  the  Fahrenheit  degree.     It  is  also  given  as 
424  kilogrammeters,  reference  being  made  to  the  centigrade  degree. 
Show  that  the  two  values  are  approximately  identical. 


366  REVIEW. 

Recapitulation.-^In  this  section  we  have  considered 
the  definition  of  Thermodynamics ;  the  Corre- 
lation of  Heat  and  Mechanical  Energy ; 
heat  from  Percussion ;  from  Friction ;  First 
Law  of  thermodynamics;  Joule's  Equivalent 
and  its  Use;  Chemical  Affinity  and  the  Heat- 
ing Powers  of  various  substances ;  the  Single  and 
Double-acting  Steam-engines ;  the  Eccen- 
tric, Governor  and  Safety-valve  ;  Condens- 
ing and  Non-condensing  Engines;  the  relation 
between  Heat  and  Work  in  the  steam-engine. 

REVIEW  QUESTIONS  AND  EXERCISES. 

1.  Lead  melts  at  326°  C.    In  melting  it  absorbs  about  as  much 
heat  as  would  warm  5.37  times  its  weight  of  water  1°C.    What 
numbers  will  replace  the  326  and  5.37  when  the  Fahrenheit  scale  is 
used? 

2.  What  is  the  difference  between  the  temperatures— 40°  C.  and 
-40°  F.  ? 

3.  A  quantity  of  gas  at  100°  C.  and  under  a  pressure  of  750  mm.  of 
mercury  measures  4500  cu.  cm.    What  will  be  its  volume  at  200C  C. 
and  under  a  pressure  of  76  cm.  of  mercury  ? 

4.  Over  how  high  a  ridge  can  you  carry  water  in  a  siphon,  where 
the  minimum  range  of  the  barometer  is  27  inches  ?    Explain. 

5.  (a.)  What  is  Specific  Gravity  ?  (&.)  How  do  you  find  that  of  solids 
heavier  than  water?    (c.)  What  principle  is  involved  in  your  method  ? 

6.  (a.)  Of  what  physical  force  is  lightning  a  manifestation?    (b.) 
Give  some  plain  directions  for  the  construction  of  lightning-rods, 
with  reasons  for  your  directions. 

7.  Give  the  fundamental  principle  of  mechanics,  and  illustrate  its 
application  by  one  of  the  mechanical  powers. 

8.  (a.)  What  are  the  essential  properties  of  matter?  (&.)  What  is  a 
pendulum  ;  (c.)  to  what  use  is  it  principally  applied,  and  (d.)  what 
are  the  laws  by  which  it  is  governed  ? 

9.  (a.)  In  what  ways  may  two  musical  tones  differ  ?    (&.)  What  is 
the  physical  cause  of  the  difference  in  each  case  ? 

10.  (a.)  Convert  -3°  F.  and  77°  F.  into  C.  readings  ;    (&.)  18°  0 
and  20°  C.  to  F.  readings. 


REVIEW.  367 

11.  (a.)  To  what  temperature  should  a  liter  of  oxygen  at  0°  C.  be 
raised  in  order  to  double  its  volume,  the  pressure  remaining  con- 
stant ?    (&.)  Give  reasons  for  your  answer. 

12.  (a.)  What  is  meant  by  the  boiling  point  of  a  liquid  ?    (6.)  State 
some  circumstances  that  cause  it  to  vary. 

13.  A  kilogram  each  of  water,  iron  and  antimony,  at  0°C.  are 
heated  ten  minutes  by  the  same  source  of  heat,  and  are  then  found 
to  be  1°  C.,  9°  C.  and  20°  C.  respectively.    Required  the  specific  heat 
of  each. 

14.  (a.)  Define  latent  heat.     (&.)  Describe  a  method  of  determining 
the  latent  heat  of  water,    (c.)  Describe  the  cooling  and  freezing  of 
a  lake. 

15.  (a.)  If  2  kilograms  of  water  should  be  suddenly  stopped  after 
falling  212  metres,   how  much  heat  would  be  generated?     (b.) 
Describe  the  essential  parts  of  a  steam-engine. 

16.  (a.)  How  many  cubic  feet  of  water  will  be  displaced  by  a  boat 
weighing  two  tons  ?     (b.)  How  many  of  salt  water  of  sp.  gr.  1.09  ? 
|c.)  How  does  a  noise  differ  from  a  musical  sound  ? 

17.  The  sp.  gr.  of  alcohol  is  .8  ;   that  of  mercury  13.6.     When  a 
mercury  barometer  indicates  a  pressure  of  30  inches,  what  will  be 
the  height  of  an  alcohol  barometer  column  ? 

18.  (a.)  Describe  the  ordinary  force-pump ;  (b.)  explain  the  use  of 
its  essential  parts. 

19.  (a.)  Give  the  formulas  for  changing  thermometric  readings 
from  F.  to  C.,  and  vice  versa,     (b.)  Explain  the  graduation  of  two 
kinds  of  thermometers,    (c.)  Define  increment  of  velocity. 

20.  («.)  What  is  distillation,  and  upon  what  fact  does  the  process 
depend?    (&.)  What  is  latent  heat?    (c.)  Illustrate  the  conversion 
of  sensible  into  latent  heat,     (d.)  On  what  does  the  pitch  of  sound 
depend  ? 

21.  (a.)  Define  boiling  and  boiling-point.    (b.)  What  is  the  rate  of 
expansion  for  gases  ?    (c. )  Will  water  boil  at  a  lower  temperature 
at  the  sea  level  or  on  the  top  of  a  mountain  ?    Why  ?    (d.)  What 
constitutes  the  timbre  of  a  sound  ?    (e.)  Give  the  formulas  for  the 
wheel  and  axle. 

22.  (a.)  If  the  pressure  remain  the  same,  how  much  will  546  cu.  cm. 
of  hydrogen  expand  when  heated  from  0°  C.  to  10°  C.  ?    (b.)  How 
mnch  work  may  be  performed  by  a  ball  weighing  64.32  Ibs.,  moving 
with  a  velocity  of  50  ft.  per  second  ?    (c.)  When  has  water  the 
greatest  density  ? 

23.  Show  that  to  raise  the  temperature  of  a  pound  of  iron  from 
0°  C.  to  100°  C.  requires  more  energy  than  to  raise  seven  tons  of  iron 
a  foot  high. 


IX. 


LIGHT. 


ECTION  I, 


THE    NATURE,    VELOCITY   AND    INTENSITY 
OF    LIGHT. 

579.  What  is  Light?— Light  is  that  mode  of 
motion    which    is    capable    of  affecting    the  optic 
nerve.     Tlie  only  physical  difference  between  light 
and  radiant  heat  is  one  of  wave  length. 

(a.)  We  have  seen  that  the  vibrations  of  air  particles  in  a  sound 
wave  are  to  and  fro  in  the  line  of  propagation.  In  the  case  o^' 
radiant  heat  and  light,  the  ether  particles  vibrate  to  and  fro  across 
the  line  of  propagation.  Vibrations  in  a  sound  wave  are  longitudi- 
nal; those  of  a  heat  or  light  wave  are  transversal. 

580.  Luminous  and  Non-Luminous  Bodies. 

— Bodies  that  emit  light  of  their  own  generating,  as  the 
sun  or  a  candle,  are  called  luminous.  Bodies  that  merely 
diffuse  the  light  that  they  receive  from  other  bodies  are 
said  to  be  non-luminous  or  illuminated.  Trees  and  plants 
are  non-luminous. 

(a.)  Visible  bodies  may  be  luminous  or  illuminated,  but  in  either 
case  they  send  light  in  every  direction  from  every  point  in  their 
surfaces.  In  Fig.  271  we  see  represented  a  few  of  the  infinite 
number  of  lines  of  light  starting  from  A,  B  and  C,  three  of  the 


THE  NATURE   OF  LIGHT.  369 

infinite  number  of  points  in  the  surface  of  a  visible  object.  If  the 
infinite  number  of  lines  were  drawn  from  each  of  the  infinite  number 
of  points,  there  would  be  no  vacant  spaces  in 
the  figure  ;  the  rays  really  intersect  at  every 
point  from  which  the  object  is  visible. 

581.  Transparent,    Translu- 
cent and  Opaque  Bodies. — Bodies 
are  transparent,  translucent  or  opaque 
according  to  the  degree  of  freedom  which 

they  afford  to  the  passage  of  the  luminiferous  waves. 
Transparent  bodies  allow  objects  to  be  seen  distinctly 
through  them,  e.  g.,  air,  glass  and  water.  Translucent 
bodies  transmit  light,  but  do  not  allow  bodies  to  be  seen 
distinctly  through  them,  e.g.,  ground  glass  and  oiled  paper. 
Opaque  bodies  cut  off  the  light  entirely  and  prevent 
objects  from  being  seen  through  them  at  all.  The  light 
is  either  reflected  or  absorbed.  So  much  of  the  radiant 
energy  as  is  neither  reflected  nor  transmitted  is  changed 
to  absorbed  heat. 

582.  Luminous  Rays. — A  single  line  of  light  is 
called  a  ray.    The  ray  of   light  is  perpendicular  to  the 
wave  of  ether.     The  ray  may,  without  considerable  error, 
be  deemed  the  path  of  the  wave. 

583.  Luminous  Beams  and  Pencils. — A  col- 
lection of  parallel  rays  constitutes  a  beam  ;  a  cone  of  rays 
constitutes  a  pencil.     The  pencil  may  be  converging  or 
diverging.    If  a  beam  or  pencil  should  dwindle  in  thick- 
ness to  a  line,  it  would  become  a  ray. 

584.  Rectilinear  Motion  of  Light.— A  medium 
is  homogeneous  when  it  has  an  uniform  composition  and 
density.    In  a  homogeneous  medium,  light  travels 


370  THE  NATURE  OF  LIGHT. 

in  straight  lines.    This  is  a  fact  of  incalculable  scien- 
tific and  otherwise  practical  importance. 

(O  The  familiar  experiment  of  "taking  sight"  depends  upon 
this  fact,  for  we  see  objects  by  the  light  which  they  send  to  the  eye. 
We  cannot  see  around  a  corner  or  through  a  crooked  tube.  A  beam 
of  light  that  enters  a  darkened  room  by  a  small  aperture,  marks  an 
illuminated  course  that  is  perfectly  straight. 

(6.)  This  fact  may  be  illustrated  by  providing  two  or  three  per- 
forated screens  and  arranging  them  as  shown  in  Fig.  272,  so  that 
the  holes  and  a  candle  flame  shall  be  in  the  same  straight  line. 


FIG.  272. 

When  the  eye  is  placed  in  this  line  behind  the  screens,  light  passes 
from  the  flame  to  the  eye  ;  the  flame  is  visible.  A  slight  displace- 
ment upward,  downward  or  sidewise  of  the.eye,  the  flame  or  any 
screen,  cuts  off  the  light  and  renders  the  flame  invisible. 

(c.)  Prepare  a  piece  of  wood,  1^  x  2^  x  18  inches,  taking  care  that 
the  edges  are  square.  Saw  it  into  six  pieces,  each  three  inches  long. 
Prepare  three  pieces  of  wood,  3  x  4  x  £  inches.  Place  three  postal 
cards  one  over  the  other  on  a  board,  and  pierce  them  with  a  fine 
awl  or  stout  needle,  \  inch  from  the  end  and  \\  inch  from  either 
side  of  the  card.  With  a  sharp  knife  pare  off  the  rough  edges  of 
the  holes,  and  pass  the  needle  through  each  hole  to  make  the  edges 
smooth  and  even.  Over  the  \  x  3  inch  surface  of  one  of  the  blocks 
place  the  unperforated  end  of  one  of  the  postal  cards,  and  over  this 
place  one  of  the  3  x  4  inch  pieces,  so  that  their  lower  edges  shall  be 


THE  NATURE   OF  LIGHT.  371 

even.  Tack  them  in  this  position.  Make  thus  two  more  similar 
screens.  The  three  screens,  with  a  bit  of  candle  three  inches  long, 
placed  upon  one  of  the  remaining  blocks,  furnishes  the  material 
for  the  experiment  above.  Save  the  screens  and  three  blocks  for 
future  use.  (See  Fig.  280.) 

585.  Inverted  Images.— If  light  from  a  highly- 
illuminated  body  be  admitted  to  a  darkened  room  through 
a  small  hole  in  the  shutter  and  there  received  upon  a  white 
screen,  it  will  form  an  inverted  image  of  the  object  upon 
the  screen.  Every  visible 
point  of  the  illuminated 
object  sends  a  ray  of  light 
to  the  screen.  Each  ray 
brings  the  color  of  the 

point  which  sends  it  and  prints  the  color  upon  the  screen. 
As  the  rays  are  straight  lines,  they  cross  at  the  aperture; 
hence,  the  inversion  of  the  image.  The  image  will  be  dis- 
torted unless  the  screen  be  perpendicular  to  the  rays. 
The  darkened  room  constitutes  a  camera  olscura.  The 
image  of  the  school  playground  at  recess  is  very  inter- 
esting and  easily  produced. 

(a.)  Place  a  lighted  candle  about  a  meter  from  a  white  screen  in  a 
darkened  room.  (The  wall  of  the  room  will  answer  for  the  screen.) 
Pierce  a  large  pin-hole  in  a  card,  and  hold  it  between  the  flame  and 
the  screen.  An  inverted  image  of  the  flame  will  be  found  upon  the 
screen. 

(b.)  Bore  an  inch  hole  in  one  side  of  a  wooden  box;  cover  this 
opening  with  tinfoil,  and  prick  the  tinfoil  with  a  needle.  Place  a 
lighted  candle  within  the  box  ;  close  the  box  with  a  lid  or  a  shawl, 
and  hold  a  paper  screen  before  the  hole  in  the  tinfoil.  Move  the 
screen  backward  and  forward,  and  notice  that  in  any  position  the 
size  of  the  object  is  to  the  size  of  the  image  as  the  distance  from 
the  aperture  to  the  object  is  to  the  distance  from  the  aperture  to  the 
image. 

(c.)  Cover  one  end  of  a  tube,  10  or  12  cm.  long,  with  tinfoil ;  the 
other  end  with  oiled  paper,  Prick  a  pin-hole  in  the  tinfoil  and  turn 


372  THE  NATURE  OF  LIGHT. 

it  toward  a  candle  flame.  The  inverted  image  may  be  seen  upon 
the  oiled  paper.  Th«  size  of  the  image  will  depend  upon  the  dis- 
tance of  the  flame  from  the  aperture.  The  apparatus  rudely  repre- 
sents the  eye,  the  pin-hole  corresponding  to  the  pupil  and  the  oiled 
paper  to  the  retina.  (Almost  any  housekeeper  will  give  you  an 
empty  tin  can.  Place  it  upon  a  hot  stove  just  long  enough  to  melt 
off  one  end,  thrust  a  stout  nail  through  the  centre  of  the  other 
end,  cover  the  nail  hole  with  tinfoil,  and  you  will  have  the  greater 
part  of  the  apparatus.) 

586.  Shadows. — Since  rays  of  light  are  straight, 
opaque  bodies  cast  shadows.  A  shadow  is  the  dark- 
ened space  behind  an  opaque  body  from  which  all 
rays  of  light  are  cut  off.  It  is  sometimes  called  the 
perfect  shadow  or  the  umbra.  If  the  source  of  light  be  a 
point,  the  shadow  will  be  well  defined ;  if  it  be  a  surface, 
the  shadow  will  be  surrounded  by  an  imperfect  shadow 
called  a  penumbra.  The  penumbra  is  the  darkened 
space  behind  an  opaque  body  from  which  some  of  the 
rays  (the  rays  from  a  part  of  the  luminous  surface)  are 
cut  off. 


FIG.  274. 

(a.)  Hold  a  lead  pencil  between  the  flame  of  an  ordinary  lamp  and 
a  sheet  of  paper  held  about  two  feet  (61  cm.)  from  the  lamp  :  (1.) 
When  the  edge  of  the  flame  is  toward  the  pencil ;  (2.)  When  the 
side  of  the  flame  is  toward  the  pencil. 


THE  NATURE  OF  LIGHT.  373 

(&.)  Describe  the  shadow  cast  by  a  sphere  and  a  luminous  point. 
By  a  sphere  and  a  luminous  globe  of  equal  size.  By  a  sphere  and 
a  luminous  globe  of  greater  size,  e.  g.,  the  earth's  shadow.  A  solar 
eclipse  takes  place  whenever  the  eye  of  the  observer  is  in  the 
shadow  of  the  moon.  Figure  the  shadow  of  the  moon.  Where 
must  the  observer  be  to  see  a  total  eclipse  of  the  sun  ?  To  see  an 
ordinary  eclipse  (when  the  sun  appears  crescent-shaped)?  To  see 
an  annular  eclipse  ? 

587.  Visual  Angle. — Tlie  angle  included  be- 
tween two  rays  of  light  coming  from  the  extrem- 
ities of  an  object  to  the  centre  of  the  eye  is  called 
the  visual  angle.  This  angle  measures  the  apparent 
length  of  the  line  that  subtends  it.  Any  cause  that 
increases  the  visual  angle  of  an  object  increases  its  appa- 
rent size.  Hence  the  effect  of  magnifying-glasses.  From 


Fig.  275  we  see  that  equal  lines  may  subtend  different 
visual  angles,  or  that  different  lines  may  subtend  the  same 
angle. 

588.  Velocity  of  Light.— Light  traverses  the  ether 
with  a  velocity  of  about  186,000  miles  or  about  298  mil- 
lion meters  per  second.  This  was  first  determined  about 
200  years  ago  by  Koemer,  a  Danish  astronomer. 

(«.)  At  equal  intervals  of  42h.  28m.  36s.,  the  nearest  of  Jupiter's 
satellites  passes  within  his  shadow  and  is  thus  eclipsed.  This  phe- 
nomenon would  be  seen  from  the  earth  at  equal  intervals  if  light 
traveled  instantaneously  from  planet  to  planet.  Roemer  found 
that  when  the  earth  was  farthest  from  Jupiter  the  eclipse  was  seen 
16  min.  36  sec.  later  than  when  the  earth  was  nearest  Jupiter.  But 
Jupiter  and  the  earth  are  nearest  each  other  when  they  are  on  the 


374  THE  NATURE  OF  LIGHT. 

same  side  of  the  sun  and  in  a  straight  line  with  the  sun  (conjunc- 
tion), and  farthest  from  each  other  when  they  are  on  opposite 
sides  of  the  sun  and  in  a  straight  line  with  that  luminary  (opposi- 


FIG.  276. 

tion).  Hence,  Roemer  argued  that  it  requires  16  min.  36  sec.  for 
light  to  pass  over  the  diameter  of  the  earth's  orbit,  from  Eio  E'. 
This  distance  being  approximately  known,  the  velocity  of  light  is 
easily  computed. 

(&.)  The  velocity  of  light  has  been  measured  by  other  means, 
giving  results  that  agree  substantially  with  the  result  above  given. 
When  astronomers  accurately  determine  the  mean  distance  of  the 
earth  from  the  sun,  the  velocity  of  light  will  be  accurately  known. 

(c.)  It  would  require  more  than  17  years  for  a  cannon-ball  to  pass 
over  the  distance  between  the  sun  and  the  earth ;  light  makes  the 
journey  in  8  min.  18  sec.  For  the  swiftest  bird  to  pass  around  the 
earth  would  require  three  weeks  of  continual  flight ;  light  goes  as 
far  in  less  than  one  seventh  of  a  second.  For  terrestrial  distances, 
the  passage  of  light  is  practically  instantaneous  (§  435). 

589.  Effect  of  Distance  upon  Intensity.— 

The  intensity  of  light  received  ~by  an  illuminated 
body  varies  inversely  as  the  square  of  its  distance 
from  the  source  of  light. 

(a.)  Let  a  candle  at  8  be  the  source  of  light ;  A,  a  screen  one  foot 
square  and  a  yard  from  S ;  B,  a  screen  two  feet  square  two  yards 
from  8',  C,  &  screen  three  feet  square  three  yards  from  S.  It 
will  easily  be  seen  that  A  will  cut  off  all  the  light  from  B  and  (7. 
If  now  A  be  removed,  the  quantity  of  light  which  it  received,  no 
more  and  no  less,  will  fall  upon  B.  If  now  B  be  removed,  the 
quantity  of  light  which  previously  illuminated  A  and  B  will  fall 
upon  (7.  We  thus  see  the  same  number  of  rays  successively  illu- 


THE  NATURE  OF  LIGHT.  375 

minating,  one,  four  and  nine  square  feet.    One  square  foot  at  B  will 

receive  one-fourth,  and  one 
square  foot  at  C  will  receive 
one-ninth  as  many  rays  as 
one  square  foot  at  A.  The 
light  being  diffused  over  a 
greater  surface  is  corres- 
pondingly diminished  in  in- 
tensity. 

(6.)  The  experiment  may 
be  tried  by  placing  the  large 
screen  at  A  and  tracing  the 
outline  of  the  shadow  with 
a  pencil,  then  placing  the 
FIG.  277.  screen  successively  at  B  and 

C,  tracing  the  shadow  each 

time.     The  experiment  will  be  more  satisfactory  if  a  perforated 

screen  be  placed  at  8. 

EXERCISES. 

1.  A  coin  is  held  5  feet  from  a  wall  and  parallel  to  it.     A  lumi- 
nous point,  15  inches  from  the  coin,  throws  a  shadow  of  it  upon  the 
wall.    How  does  the  size  of  the  shadow  compare  with  that  of  the  coin  ? 

2.  (a.)  What  is  the  velocity  of  light  ?    (6.)  How  was  it  determined  ? 

3.  («.)  How  are  the  intensities  of  two  lights  compared  ?    (&.)  De- 
fine light,    (c.)  Give  your  idea  of  the  carrier  of  radiant  heat  and  light. 

4.  (a.}  Define  luminous,  transparent,  opaque,  beam  and  pencil. 
(ft.)  How  could  you  show  that  light  ordinarily  moves  in  straight 
lines  ?    (c.)  Explain  the  formation  of  inverted  images  in  a  dark  room. 

5.  («.)  What  are  shadows  ?      (&.)  By  figures,  illustrate  shadows 
when  the  intercepting  body  is  greater,  equal  to  and  less  than  the 
luminous  body,  and  explain,     (c.)  What  is  the  visual  angle  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Nature  of  Light ;  Luminous,  Illuminated, 
Transparent,  Translucent  and  Opaque  bodies ; 
Rays,  Beams  and  Pencils  of  light;  that  Light 
Moves  in  Straight  Lines;  Inverted  Images 
and  Shadows  ;  the  Visual  Angle  ;  the  Veloc- 
ity and  Intensity  of  light. 


376  TltE  NATURE   OF  LIGHI. 

ECTION  II. 


Si 

REFLECTION    OF    LIGHT. 

Note.— The  heliostat,  or  porte-lumiere,  is  composed  of  one  or 
more  mirrors,  by  means  of  which  a  beam  of  light  may  be  thrown 
in  any  desired  direction.  The  instrument  may  be  had  of  apparatus 
manufacturers  at  prices  ranging  from  $12  upward.  Directions  for 
making  one  may  be  found  in  Mayer  &  Barnard's  little  book  on 
"  Light,"  published  by  D.  Appleton  &  Co.  It  is  very  desirable  that 
the  instrument  be  secured  in  some  way. 

59 O.  Reflection. — If  a  sunbeam  enter  a  darkened 
room  by  a  hole  in  the  shutter,  as  at  A,  and  fall  upon  a 


FIG.  278. 

polished  plane  surface,  as  at  B,  it  will  be  continued  in  a 
different  direction,  as  toward  C.  AB  is  called  the  incident 
beam  and  BC  the  reflected  beam  (§  97).  The  incident 
and  the  reflected  beams  are  in  the  same  medium,  the  air. 
A  change  in  the  direction  of  light  without  a  change 
in  its  medium  is  called  reflection  of  light. 

591.  Laws  of  Reflection. — The  reflection  of  light 


REFLECTION  OF  LIGHT.  377 

from  polished  surfaces  is  in  accordance  with  the  following 
laws: 

(1.)  The  angle  of  incidence  is  equal  to  the  angle 
of  reflection. 

(2.)  The  incident  and  reflected  rays  are  both  in 
the  same  plane,  which  is  perpendicular  to  the 
reflecting  surface. 

(a.)  Fill  a  basin  to  the  brim  with  mercury  or  with  water  blackened 
with  a  little  ink.  In  this  liquid  suspend  by  a  thread  a  small 
weight  of  greater  specific  gravity  than  the  liquid  used  (§  253).  The 
plumb-line  will  be  perpendicular  to  the  liquid  mirror.  Let  the 
plumb-line  hang  from  the  middle  of  a  horizontal  meter  or  yard- 


FIG.  279. 


stick.  Place  the  tip  of  a  candle  flame  opposite  one  of  the  divisions 
of  the  stick,  and  place  the  eye  in  such  a  position  that  the  image  of 
the  top  of  the  flame  will  be  seen  in  the  direction  of  the  foot  of 
the  plumb-line.  Mark  the  point  where  the  line  of  vision  (i.  e.,  the 
reflected  rays)  crosses  the  meter-stick.  It  will  be  found  that  this 
point  and  the  tip  of  the  flame  are  equally  distant  from  the  middle 
of  the  stick.  From  this  it  follows  (Olney's  Geometry,  Art.  342) 
that  the  angles  of  incidence  and  of  reflection  are  equal. 

(&.)  Fig.  279  represents  a  vertical  semicircle  graduated  to  degrees, 
with  a  background  of  black  velvet.  A  mirror  at  the  centre  is 
furnished  with  an  index  set  perpendicular  to  its  plane  ;  both  mirror 
and  index  can  be  turned  in  any  direction  desired.  A  ray  of  light 
from  any  brilliant  source  is  allowed  to  enter  the  tube  at  the  base, 
in  the  direction  of  the  centre.  By  means  of  a  little  smoke  from 
brown  paper,  the  paths  of  the  incident  and  reflected  rays  are  easily 
shown  to  a  large  class. 


378  REFLECTION  OF  LIGHT. 

(c.)  Place  two  of  the  screens  and  the  three  extra  blocks  men- 
tioned in  §  584  in  position,  as  shown  in  Fig.  280.  At  the  middle 
of  the  middle  block  place  a  bit  of  window  glass,  painted  on  the 
under  side  with  black  varnish.  On  the  blocks  that  carry  the  screens 
place  bits  of  glass,  n  and  o,  of  the  same  thickness  as  the  black  mir- 
ror on  the  middle  block.  Place  a  candle  flame  near  the  hole  in  one 
of  the  screens,  as  shown  in  the  figure.  Light  from  the  candle  will 
pass  through  A,  be  reflected  at  m,  and  pass  through  B.  Place  the 
eye  in  such  a  position  that  the  spot  of  light  in  the  mirror  may 
be  seen  through  B.  Mark  the  exact  spot  in  the  mirror  with  a 
needle  held  in  place  by  a  bit  of  wax.  Place  a  piece  of  stiff  writing 
paper  upright  upon  m  and  n,  mark  the  position  of  B  and  of  m, 
and  draw  on  the  paper  a  straight  line  joining  these  two  points. 
The  angle  between  this  line  and  tho  lower  edge  of  the  paper 
coincides  with  the  angle  Bmn.  Reverse  the  paper,  placing  it  upon 


FIG.  280. 

m  and  o.  It  will  be  found  that  the  same  angle  coincides  with 
Amo.  Amo  and  Bmn  being  thus  equal,  the  angle  of  incidence 
equals  the  angle  of  reflection. 

592.  Diffused  Light. — Light  falling  upon  an 
opaque  body  is  generally  divided  into  three  parts  :  the 
first  is  regularly  reflected  in  obedience  to  the  laws  above ; 
the  second  is  irregularly  reflected  or  diffused  ;  the  third  is 
absorbed.  The  irregular  reflection  is  due  to  the  fact  that 
the  bodies  are  not  perfectly  smooth,  but  present  little  pro- 
tuberances that  scatter  the  light  in  all  directions,  and  thus 
render  them  visible  from  any  position.  Light  regularly 
reflected  gives  an  image  of  the  body  from  which  it  came 
before  reflection  :  light  irregularly  reflected  gives  an  image 


REFLECTION  OF  LIGHT.  379 

of  the  body  that  diffuses  it.  A  perfect  mirror  would  be 
invisible.  Luminous  bodies  are  visible  on  account 
of  the  light  that  they  emit;  non-luminous  bodies 
are  visible  on  account  of  the  light  that  they  dif- 
fuse. 

(a.)  If  a  beam  of  light  fall  upon  a  sheet  of  drawing  paper,  it 
will  be  scattered  and  illuminate  a  room.  If  it  fall  upon  a  mirror, 
nearly  all  of  it  will  be  reflected  in  a  definite  direction,  and  intensely 
illuminate  a  part  of  the  room.  Place  side  by  side  upon  a  board 
a  piece  of  black  cloth  (not  glossy),  a  piece  of  drawing  paper  and  a 
piece  of  looking-glass.  In  a  darkened  room,  allow  a  beam  of  sun- 
light to  fall  upon  the  cloth  and  notice  the  absorption.  Let  it  fall 
upon  the  paper,  and  notice  the  diffusion  of  the  light  and  its  effects. 
Let  it  fall  upon  the  looking-glass,  and  notice  the  regular  reflection 
and  its  effects.  Move  the  board  so  that  the  cloth,  paper  and  glass 
shall  pass  through  the  beam  in  quick  succession,  and  notice  the 
effects. 

(&.)  In  the  darkened  room  place  a  tumbler  of  water  upon  a  table  ; 
with  a  hand-mirror  reflect  a  sunbeam  down  into  the  water;  the 
tumbler  will  be  visible.  Stir  a  teaspoonful  of  milk  into  the  water, 
and  again  reflect  the  sunbeam  into  the  liquid  ;  the  whole  room  will 
be  illuminated  by  the  diffused  light,  the  tumbler  of  milky  water 
acting  like  a  luminous  body. 

593.  Invisibility  of  Light.—  Rays  of  light  that 
do  not  enter  the  eye  are  invisible.  A  sunbeam 
entering  a  darkened  room  is  visible  because  the  floating 
dust  reflects  some  of  the  rays  to  the  eye.  If  the  reflecting 
particles  of  dust  were  absent  the  beam  would  be  invisible. 


(a.)  Take  any  convenient  box,  about  60  cm.  (2/£.)  on  each  edge, 
provide  for  it  a  glass  front,  and,  at  each  end,  a  glass  window  about 
10  cm.  (4  inches)  square.  Place  it  on  a  table  in  a  darkened  room, 
and,  with  the  heliostat,  send  a  solar  beam  through  the  windows. 
Standing  before  the  glass  front  of  the  box,  this  beam  may  be 
traced  from  the  heliostat  to  the  box,  -through  the  box  and  beyond 
it.  Open  the  box,  smear  the  inner  surfaces  of  its  top,  back  and 
bottom  with  glycerine,  and  close  the  box  air-tight.  Allow  it  to 
remain  quiet  a  few  days  ;  the  dust  in  the  box  will  be  caught  by 
the  glycerine  and  the  confined  air  thus  freed  from  particles  capable 


380  REFLECTION  OF  LIGHT. 

of  reflecting  light.  Then  send  another  solar  beam  from  the  helio- 
stat  through  the  two  windows  of  the  box.  Standing  as  before, 
the  beam  may  be  traced  to  the  box  and  beyond  it,  but  within  the 
box  all  is  darkness. 

594.  Apparent  Direction  of  Bodies.— Every 

point  of  a  visible  object  sends  a  cone  of  rays  to  the  eye. 
The  pupil  of  the  eye  is  the  base  of  the  cone.  TJie  point 
always  appears  at  the  place  where  these  rays  seem 
to  intersect  (i.  e.,  at  the  real  or  apparent  apex  of  the  cone). 
If  the  rays  pass  in  straight  lines  from  the  point  to  the  eye, 
the  apparent  position  of  the  point  is  its  real  position.  If 
these  rays  be  bent  by  reflection,  or  in  any  other  manner, 
the  point  will  appear  to  be  in  the  direction  of 
the  rays  as  they  enter  the  eye.  No  matter  how 
devious  the  path  of  the  rays  in  coming  from  the  point  to 
the  eye,  this  important  rule  holds  good. 

595.  Plane  Mirrors;  Virtual  Images. — If  an 

object  be  placed  before  a  mirror,  an  image  of  it  appears 

behind  the  mirror.  In- 
asmuch as  the  rays  of 
the  cone  mentioned  in 
§  594  do  not  actually  con- 
verge back  of  the  mirror, 
there  can  be  no  real  image 
there.  As  there  really  is 
no  image  behind  the  mir- 
ror, we  call  it  a  virtual 

image.    All  virtual  images 
FIG.  281.  , .    ,  .,,     .  .. 

are  optical  illusions,  and 

are  to  be  clearly  distinguished  from  the  real  images  to  be 
studied  soon.  Each  point  of  this  linage  will  seem 
to  be  as  far  behind  the  mirror  as  the  correspond- 


REFLECTION  OF  LlGBT.  381 

ing  point  of  the  object  is  in  front  of  the  mirror. 
Hence,  images  seen  in  still,  clear  water  are  inverted. 

(a.)  In  Fig.  281,  let  A  represent  a  luminous  point ;  MM,  a  mirror  ; 
A  A'  and  BC,  lines  perpendicular  to  the  mirror.  Rays  from  A  enter 
the  eye  at  DD'.  The  angle  ABC  =  the  angle  CBD  (§  591).  The 
angle  ABC  =  the  angle  BAA'  (Olney's  Geometry,  Art.  150).  There- 
fore the  angle  CBD  -  the  angle  BAA.  The  angle  CBD  =  the  angle 
BAA  (Olney,  152).  Therefore  the  angle  BA A  =  the  angle  BAA. 
Hence  AM=  A M  (Olney,  287).  In  other  words,  A'  is  as  far  behind 
the  mirror  as  A  is  in  front  of  it. 

(6.)  Place  a  jar  of  water  10  or  15  cm.  back  of  a  pane  of  glass  placed 
upright  on  a  table  in  a  dark  room.  Hold  a  lighted  candle  at  the 
same  distance  in  front  of  the  glass.  The  jar  will  be  seen  by  light 
transmitted  through  the  glass.  An  image  of  the  candle  will  be 
formed  by  light  reflected  by  the  glass.  The  image  of  the  candle 
will  be  seen  in  the  jar,  giving  the  appearance  of  a  candle  burning 
in  water.  The  same  effect  may  be  produced  in  the  evening  by  partly 
raising  a  window  and  holding  the  jar  on  the  outside  and  the  candle 
on  the  inside. 

596.  Reflection  of  Kays  from  Plane  Mir- 
rors.— If  the  incident  rays  be  parallel,  the  reflected  rays 
will  be  parallel.    If  the  incident  rays  be  diverging,  the 
reflected  rays  will  be  diverging ;  they  will  seem  to  diverge 
from  a  point  as  far  behind  the  reflecting  surface  as  their 
source  is  in  front  of  that  surface  (See  Fig.  281).     If  the 
incident  rays  be  converging,  the  reflected  rays  will  be  con- 
verging ;  they  will  converge  at  a  point  as  far  in  front  of 
the  mirror  as  the  point  at  which  they  were  tending  to 
converge  is  behind  the  mirror. 

597.  Construction    for    the    Image    of  a 
Plane  Mirror. — The  position  of  the  image  of  an  object 
may  be  determined  by  locating  the  images  of  several  well-- 
chosen points  in  the  object  and  connecting  these  images. 

(a.)  In  Fig.  282,  let  AB  represent  an  arrow  ;  MN,  the  reflecting 
surface  of  a  plane  mirror,  and  E  the  eye  of  the  observer.  From 


382 


REFLECTION  OF  LIGHT. 


FIG.  282. 


A,  draw  Aa  perpendicular  to  MN  and  make  ad  equal  to  Ad.  Then 
will  a  indicate  the  position  of  the  image 
of  A.  From  B,  draw  Bb  perpendicular 
to  MN  and  make  be  equal  to  Be.  Then 
will  b  indicate  the  position  of  the  image 
of  B.  By  connecting  a  and  b  we  locate 
the  image  of  AB.  Draw  aE,  bJS,  Ao 
and  BL  AoE  represents  one  ray  of  the 
cone  of  rays  from  A  that  enters  the  eye  ; 
BiE  represents  one  ray  of  a  similar  cone 
from  B.  Draw  a  similar  figure  on  a 
larger  scale,  representing  the  eye  at  C . 

Test  your  figure  by  seeing  if  the  angle  of  incidence  is  equal  to  the 

angle  of  reflection.     In  all  such  constructions,  represent  the  direction 

of  the  rays  by  arrow-heads,  as  shown  in  Fig.  282. 

598.  Multiple  Images. — By  placing  two  mirrors 
facing  each  other,  we  may  produce  multiple  images  of 
an    object   placed  between   them.      Each   image  acts 
as    a    material    object    with    respect   to    the    other 
mirror,  in  which    we    see    an   image   of  the  first 
image.    When  the  mirrors  are  placed  so  as  to  form  an 
angle  with  each  other,  the  number  of  images  becomes 
limited,  being  one  less  than  the  number  of  times  that  the 
included  angle  is  contained  in  four 

right  angles.  The  mirrors  will  give 
three  images  when  placed  at  an  angle 
of  90°;  five  at  60° ;  seven  at  45°. 

(a.)  When  the  mirrors  are  placed  at  right 
angles  the  object  and  the  three  images  will 
be  at  the  corners  of  a  rectangle  as  shown  at  a 
A,  a,  a'  and  a".  FlG-  283- 

599.  Concave    Mirrors.  — A  spherical    concave 
mirror  may  be  considered  as  a  small  part  of  a  spherical 
shell  with  its  inner  surface  highly  polished.     Let  MN  (Fig. 
284)  represent  the  section  of  such  a  concave  spherical  mir- 


REFLECTION  OF  LIGHT.  383 

ror,  and  C  the  centre  of  the  corresponding  sphere.  O  is  called 
the  centre  of  curvature;  A  is  the  centre  of  the  mirror.  A 
straight  line  of  indefinite  length  drawn  from  A  through 
C,  as  ACX,  is  called  the  principal  axis  of  the  mirror.  A 
straight  line  drawn  from  any  other  point  of  the  mirror 
through  (7,  as 
JCd,  is  called  a 
secondary  axis. 
The  point  F, 
midway  between 

A 


'  FIG. 

called  the  prin- 

cipal focus.  The  distance  AF  is  the  focal  distance  of  the 
mirror  ;  the  focal  distance  is,  therefore,  one-half  the  radius 
of  curvature.  The  angle  MCN  is  called  the  aperture  of 
the  mirror. 

(a.)  A  curved  surface  may  be  considered  as  made  up  of  an  infinite 
number  of  small  plane  surfaces.  Thus,  a  ray  of  light  reflected  from 
any  point  on  a  curved  mirror  may  be  considered  as  reflected  from  a 
plane  tangent  to  the  curved  surface  at  the  point  of  reflection.  This 
reflection  then  takes  place  in  accordance  with  the  principles  laid 
down  in  §  591.  It  should  be  borne  in  mind  that  the  radii  drawn 
from  C  to  points  in  the  mirror  as  /  and  J  are  perpendicular  to  the 
mirror  at  thesfc  points.  Thus,  the  angles  of  incidence  and  reflection 
for  any  ray  may  be  easily  determined. 

GOO.  Effect  of  Concave  Mirrors.—  The  ten- 
dency of  a  concave  mirror  is  to  increase  the  con- 
vergence or  to  decrease  the  divergence  of  incident 
rays. 

(a.)  If  the  divergence  be  that  of  rays  issuing  from  the  principal 
focus,  the  mirror  will  exactly  overcome  it  and  reflect  them  as  par- 
allel rays.  If  the  divergence  be  greater  than  this,  viz.,  that  of  rays 
issuing  from  a  point  nearer  the  mirror  than  the  principal  focus,  the 
mirror  cannot  wholly  overcome  the  divergence,  but  will  diminish  it. 


384  REFLECTION  OF  LIGHT. 

The  reflected  rays  will  still  diverge,  but  not  so  rapidly  as  the  incident 
rays.  If  the  divergence  be  less  than  that  first  mentioned,  viz.,  that 
of  rays  issuing  from  a  point  further  from  the  mirror  than  the  prin- 
cipal focus,  the  divergence  will  be  changed  to  convergence  and  a 
real  focus  will  be  formed. 

601.  The  Principal  Focus.— The  focus  of  a  con- 
cave mirror  is  the  point  toward  which  the  reflected  rays 
converge.     All  incident  rays  parallel  to  the  principal  axis 
will,  after  reflection,  converge  at  the  principal  focus.    The 
principal  focus  is  the  focus  of  rays  parallel  to  the 
principal  axis.    The  rays  will  be  practically  parallel 
when  their  source  is  at  a  very  great  distance,  e.  g.,  the  sun's 
rays.     Solar  rays  coming  to  the  human  eye  do  not  diverge 
a  thousandth  of  an  inch  in  a  thousand  miles. 

(a.)  Above  we  stated  that  parallel  rays  would  be  made  to  converge 
at  the  principal  focus  of  a  spherical  concave  mirror.  This  is  only 
approximately  true ;  it  is  strictly  true  in  the  case  of  a  parabolic 
mirror.  In  order  that  the  difference  between  the  spherical  and  the 
parabolic  mirror  may  be  reduced  to  a  minimum,  the  aperture  of  a 
spherical  mirror  must  be  small.  The  case  is  somewhat  analogous 
to  the  coincidence  of  a  circular  arc  of  small  amplitude  with  the 
cycloidal  curve  (§  144,  a).  A  source  of  light  placed  at  the  focus  of 
a  parabolic  mirror  will  have  its  rays  reflected  in  truly  parallel  lines. 
The  head  lights  of  railway  locomotives  are  thus  constructed.  Para- 
bolic mirrors  would  be  more  common  if  it  were  not  so  difficult  to 
make  them  accurately. 

602.  Conjugate    Foci. — Kays  diverging  from  a 
luminous  point  in  front  of  a  concave  spherical  mirror  and 
at  a  distance  from  the  mirror  greater  than  its  focal  distance, 
will  converge,  after  reflection,  at  another  point.    The  focus 
thus  formed  will  be  in  a  line  drawn  through  the  luminous 
point  and  the  centre  of  curvature.    In  other  words,  if  the 
luminous  point  lie  in  the  principal  axis,  the  focus  will  also  ; 
if  the  luminous  point  lie  in  any  secondary  axis,  the  focus 
will  lie  in  the  same  secondary  axis.    The  distinction  be- 


REFLECTION  OF  LIGHT. 


385 


tween  principal  and  secondary  axes  is  almost  wholly  one 
of  convenience.  Rays  diverging  from  B  will  form  a  focus 
at  b.  The  angle  of  incidence  being  necessarily  equal  to  the 


FIG.  285. 

angle  of  reflection,  it  is  evident  that  rays  diverging  from  b 
would  form  a  focus  at  B.  On  account  of  this  relation 
between  two  such  points,  they  are  called  conjugate  foci. 
Therefore,  conjugate  foci  are  two  points  so  related 
that  each  forms  the  image  of  the  other. 

603.  Construction  for  Conjugate  Foci.— In  the  case 
of  concave  mirrors,  to  locate  the  conjugate  focus  of  a  luminous 
point,  it  is  necessary  to  find  the  point  at  which  at  least  two  reflected 
rays  really  or  apparently  intersect.  The  method  may  be  illustrated 
as  follows : 


FIG.  286. 

(1.)  Let  8  (Fig.  286)  represent  the  luminous  point  whose  con- 
jugate focus  is  to  be  located.    It  may  or  may  not  lie  in  the  principal 
axis.     Draw  the  axis  for  the  point  8,  i.e.,  a  line  from  S  through  (7, 
17 


REFLECTION  OF  LIGHT. 


the  centre  of  curvature,  to  the  mirror.  This  line  represents  one  of 
the  infinite  number  of  rays  sent  from  8  to  the  mirror.  As  this 
incident  ray  is  perpendicular  to  the  mirror,  the  reflected  ray  will 
coincide  with  it.  (Angles  of  incidence  and  of  reflection  =  0.)  The 
conjugate  focus  must  therefore  lie  in  a  line  drawn  through  8  and  C. 
Draw  a  line  representing  some  other  ray,  as  Si.  From  i,  the  point 
of  incidence,  draw  the  dotted  perpendicular  iC.  Construct  the 
angle  Cis  equal  to  the  angle  CiS.  Then  will  is  represent  the  direc- 
tion of  the  reflected  ray.  The  focus  must  also  lie  in  this  line.  The 
intersection  of  this  line  with  the  line  drawn  through  SC  marks  the 
position  of  *,  the  conjugate  focus  of  8. 

(2.)  If  the  reflected  rays  be  parallel,  of  course  no  focus  can  be 
formed.  If  they  be  divergent,  produce  them  back  of  the  mirror  as 
dotted  lines  (Fig.  237)  until  they  intersect.  In  this  case  the  focus 
will  be  virtual,  because  the  rays  only  seem  to  meet.  In  the  other 
cases  the  focus  was  real,  because  the  rays  actually  did  meet. 


FIG.  287. 

(8.)  With  a  radius  of  4  cm.,  describe  ten  arcs  of  small  aperture  to 
represent  the  sections  of  spherical  concave  mirrors.  Mark  the 
centres  of  curvature  and  principal  foci,  and  draw  the  principal 
axes.  Find  the  conjugate  foci  for  points  in  the  principal  axis 
designated  as  follows  :  (1.)  At  a  distance  of  1  cm.  from  the  mirror. 
(3)  Two  cm.  from  the  mirror.  (3.)  Three  cm.  from  the  mirror. 
(4.)  Four  cm.  from  the  mirror.  (5.)  Six  cm.  from  the  mirror. 
Make  five  similar  constructions  for  points  not  in  the  principal  axia 
Notice  that  each  effect  is  in  consequence  of  the  equality  between 
the  angle  of  incidence  and  the  angle  of  reflection. 

6O4.  Formation  of  Images.— Concave  mirrors 
give  rise  to  two  kinds  of  images,  real  and  virtual.  After 


OF  LI&ffT.  387 


learning  what  has  been  said  concerning  conjugate,  real  and 
virtual  foci,  the  formation  of  these  images  will  be  easily 
understood.  The  image  of  an  object  is  determined  by 
finding  the  images  of  a  number  of  points  in  the  object. 

OO5.  Construction  for  Real  Images  Formed  by 
Concave  Mirrors.—;!.)  The  method  may  be  illustrated  as 
follows  :  Let  AS  represent  an  object  in  front  of  a  concave  mirror, 
at  a  distance  greater  than  the  radius  of  curvature.  Draw  Ax,  the 
secondary  axis  for  the  point  A.  The  conjugate  focus  of  A  will  lie 
in  this  line  (§  603  [I]).  From  the  infinite  number  of  rays  sent 
from  A  to  the  mirror,  select,  as  the  second,  the  one  that  is 
parallel  to  the  principal  axis.  This  ray,  after  reflection  at  i,  will 
pass  through  the  principal  focus  (§  601).  The  reflected  rays,  iF  and 
xA  (secondary  axis  for  A),  will  intersect  at  «,  which  is  the  ~con- 


jugate  focus  for  A  In  similar  manner,  b,  the  conjugate  focus  for 
B,  may  be  found.  Points  between  A  and  B  will  have  their  con- 
jugate foci  between  a  and  b. 

(2.)  If  the  eye  of  the  observer  be  placed  far  enough  back  of  the 
image  thus  formed  for  all  of  the  image  to  lie  between  the  eye  and 
the  mirror,  it  will  receive  the  same  impression  from  the  reflected 
rays  as  if , the  image  were  a  real  object.  All  of  the  rays  from  any 
point  in  the  object,  as  A,  that  fall  upon  the  mirror,  intersect  after 
reflection  at  a,  the  conjugate  focus.  These  reflected  rays,  after 
intersecting  at  a,  form  a  divergent  pencil.  A  cone  of  these  rays 
thus  diverging  from  a  enters  the  eye.  They  originally  diverged 


388 


REFLECTION  OF  LIGHT. 


from  A,  but  as  they  enter  the  eye,  they  diverge  from  a.  Hence  the 
effect  produced  (§  594). 

(3.)  From  the  similar  triangles,  ABC  and  abC,  it  is  evident  that 
the  linear  dimensions  of  the  object  and  of  its  image  are  directly 
proportional  to  their  distances  from  the  centre  of  curvature.  It 
may  also  be  proved  that  the  length  of  the  object  is  to  the  length  of 
the  image  as  the  distance  of  the  object  from  the  principal  focus  is 
to  the  focal  distance  of  the  mirror. 

(4.)  Since  the  lines  that  join  corresponding  points  of  object  and 
image  cross  at  the  centre  of  curvature,  the  real  images  formed  by 
concave  mirrors  are  always  inverted. 


FIG.  289. 

6O6.  Projection  of  Real  Images  by  Con- 
cave Mirrors*— The  real  image  formed  by  a  concave 
mirror  may  be  rendered  visible  even  when  the  eye  of  the 
observer  is  not  in  the  position  mentioned  in  the  last  article, 
by  projecting  it  upon  a  screen.  In  a  darkened  room,  let  a 
candle  flame  be  placed  in  front  of  a  concave  mirror,  at  a 
distance  from  it  greater  than  the  focal  distance.  Incline 
the  mirror  so  that  the  flame  shall  not  be  on  the  principal 
axis.  Place  a  paper  screen  at  the  conjugate  focus  of  any 


REFLECTION  OF  LIGHT.  389 

point  in  the  luminous  object.  The  proper  position  for  the 
screen  may  easily  be  found  by  trial.  Shield  the  screen  from 
the  direct  rays  of  the  flame  by  a  card  painted  black.  The 
inverted  image  may  be  seen  by  a  large  class.  If  the  image 
fall  between  the  mirror  and  the  candle,  the  screen  should 
be  quite  small. 

6O7.  Description  of  Real  Images  Formed 
by  Concave  Mirrors.— (1.)  If  the  object  be  at  the 
principal  focus  there  will  be  no  image.  Why  ?  (You  can 
find  out  by  trying  a  construction  for  the  image  (§  C05). 
(2.)  If  the  object  be  between  the  principal  focus  and  the 
centre  of  curvature,  the  image  will  be  beyond  the  centre, 
inverted  and  enlarged.  The  nearer  the  object  is  to  the  prin- 
cipal focus,  the  larger  and  the  further  removed  the  image 
will  be.  (3.)  When  the  object  is  at  the  centre,  the  image 
is  inverted,  of  the  same  size  as  the  object  and  at  the  same 
distance  from  the  mirror.  (4.)  When  the  object  is  not 
very  far  beyond  the  centre  of  curvature,  the  image  will 
be  inverted,  smaller  than  the  object,  and  between  the 
centre  and  the  principal  focus.  (5.)  When  the  object  is 
at  a  very  great  distance,  all  of  the  rays  will  be  practically 
parallel ;  there  will  be  but  one  focus,  and  consequently  nc 
image. 

(a.)  For  each  of  these  five  cases  construct  the  images.  The  third 
case  may  be  prettily  illustrated  as  follows  :  In  front  of  the  mirror, 
at  a  distance  equal  to  the  radius  of  curvature,  place  a  box  that  is 
open  on  the  side  toward  the  mirror.  Within  this  box  hang  an 
inverted  bouquet  of  bright-colored  flowers.  The  eye  of  the  observer 
is  to  be  in  the  position  mentioned  in  §  605  (2).  By  giving  the  mirror 
a  certain  inclination,  easily  determined  by  trial,  an  image  of  the 
invisible  bouquet  will  be  seen  just  above  the  box.  A  glass  vase 
may  be  placed  upon  the  box  so  that  it  may  seem  to  hold  the  imaged 
flowers. 


390  REFLECTION  OF  LIGHT. 

608.  Construction  for  Virtual  Images  formed  by 
Concave  Mirrors.— Let  AB  represent  an  object  in  front  of  a 
concave  mirror  at  a  distance  from  it  less  than  the  focal  distance. 
Draw  the  secondary  axes  for  the  points  A  and  B,  and  produce  them 
back  of  the  mirror  as  dotted  lines.  From  A  and  B,  draw  the  inci- 
dent rays  Ao  and  Bi,  parallel  to  the  principal  axis.  After  reflection 
they  will  pass  through  the  principal  focus  (§601 )  Produce  these 
rays  back  of  the  mirror  as  dotted  lines  until  they  intersect  the 
prolongations  of  the  secondary  axes  at  a  and  b,  which  will  be  the 
virtual  conjugate  foci  for  A  and  B.  The  conjugate  foci  for  other 
points  in  AB  will  be  between  a  and  b.  Therefore,  if  the  object  be 
between  the  principal  focus  and  the  mirror,  the  image  will  be 
virtual,  erect  and  enlarged. 


FIG.  290. 

6O9.  Images  of  the  Observer  formed  by  a 
Concave  Mirror. — A  person  at  a  considerable  distance 
before  a  concave  mirror,  sees  his  image,  real,  inverted  and 
smaller  than  the  object.  As  he  approaches  the  centre  of 
curvature,  the  image  increases  in  size.  As  the  observer 
moves  from  the  centre  to  the  principal  focus,  the  image  is 
formed  back  of  him  and  is,  therefore,  invisible  to  him.  As 
he  moves  from  the  principal  focus  toward  the  mirror,  the 
image  becomes  virtual,  erect  and  magnified,  but  gradually 
growing  smaller.  The  eye  will  not  always  recognize  real 
images  as  being  in  front  of  the  mirror.  It  may  some- 


REFLECTION  OF  LIGHT.  391 

times  be  aided  in  this  respect  by  extending  the  outspread 
fingers  between  the  image  and  the  mirror. 

61O.  Convex  Mirrors. —  In  convex  mirrors,  the 
foci  are  all  virtual;  the  images  are  virtual,  erect  and 
smaller  than  their  objects.  The  foci  may  be  found  and 
the  images  determined  by  the  means  already  set  forth. 
The  construction  is  made  sufficiently  plain  by  Fig.  291. 


FIG.  291. 

Note.— In  constructions  for  carved  mirrors,  we  have  chosen  two 
particular  rays  for  each  focus  sought ;  one  perpendicular  to  the 
mirror,  the  other  parallel  to  the  principal  axis.  This  was  onlj  for 
the  sake  of  convenience.  Any  two  or  more  incident  rajs  might 
have  been  taken  and  the  direction  of  the  reflected  rajs  determined 
bj  making  the  angle  of  reflection  equal  to  the  angle  of  incidence. 

EXERCISES. 

1.  What  must  be  the  angle  of  incidence  that  the  angle  between 
the  incident  and  the  reflected  rays  shall  be  a  right  angle  ? 

2.  The  radius  of  a  concave  mirror  is  18  inches.    Determine  the 
conjugate  focus  for  a  point  on  the  principal  axis,  12  inches  from 
the  mirror. 

3.  (a.)  Illustrate  by  a  diagram  the  image  of  an  object  placed  at  the 
principal  focus  of  a  concave  mirror ;  (b.)  of  one  placed  between 
that  focus  and  the  mirror ;  (e.)  of  one  placed  between  the  focus  and 
the  centre  of  the  mirror. 


392  REFLECTION  OF  LIGHT. 

4.  (a.)  What  kind  of  mirror  always  makes  the  image  smaller  that 
the  object?     (6.)  What  kind  of  a  mirror  may  make  it  larger  or 
smaller,  and  according  to  what  circumstances  ? 

5.  Rays  parallel  to  the  principal  axis  fall  upon  a  convex  mirror. 
Draw  a  diagram  to  show  the  course  of  the  reflected  rays. 

6.  (a.)  Why  do  images  formed  by  a  body  of  water,  appear  in- 
verted?   (6.)  What  is  the  general  effect  of  concave  mirrors  upon 
incident  rays  ? 

7.  A  person,  placed  at  a  considerable  distance  before  a  concave 
mirror,  sees  his  image,    (a.)  How  does  it  appear  to  him  ?    He  ap- 
proaches the  mirror  and  the  image  changes.    (&.)  Describe  the 
changes  that  take  place  until  he  sees  a  virtual  image  of  himself. 

8.  A  man  stands  before  an  upright  plane  mirror  and  notices  that 
he  cannot  see  a  complete  image  of  himself,    (a.)  Could  he  see  a 
complete  image  by  going  nearer  the  mirror?    Why  ?    (&.)  By  going 
further  from  it  ?    Why  ? 

9.  When  the  sun  is  3(T  above  the  horizon,  its  image  is  seen  in  a 
tranquil  pool.     What  is  the  angle  of  reflection  ? 

10.  A  person  stands  before  a  common  looking-glass  with  the  left 
eye  shut.    He  covers  the  image  of  the  closed  eye  with  a  wafer  on 
the  glass.     Show  that  when,  without  changing  his  position,  he 
opens  the  left  and  closes  the  right  eye,  the  wafer  will  still  cover  the 
image  of  the  closed  eye. 

11.  The  distance  of  an  object  from  a  convex  mirror  is  equal  to  the 
radius  of  curvature.     Show  that  the  length  of  the  image  will  be 
one-third  that  of  the  object. 

Recapitulation. — In  this  section  we  have,  considered 
the  Nature  and  Laws  of  Reflection;  Dif- 
fused and  Invisible  light;  the  Apparent  Direc- 
tion of  bodies;  Images  formed  in  Plane  Mirrors 
and  their  Construction  ;  Concave  Mirrors, 
their  Effects,  Principal  and  Conjugate  Foci; 
Images  formed  by  them  with  their  Construction, 
Projection  and  Description;  foci  and  images  for 
Convex  Mirrors. 


REFRACTION  OF  LIGHT. 


393 


ECTION  ill. 


REFRACTION    OF    LIGHT 

611.  Preparatory. — So  far,  we  have  considered  only 
that  part  of  the  incident  beam  that  is  turned  back  from 
the  reflecting  surface.  As  a  general  thing,  a  part  of  the 
beam  enters  the  reflecting  substance,  being  rapidly  absorbed 
when  the  substance  is  opaque  and  freely  transmitted  when 
the  substance  is  transparent.  We  have  now  to  consider 
those  rays  that  enter  a  transparent  substance. 

(a.)  Procure  a  clear  glass  bottle  with  flat  sides,  about  4  inches 
(10  cm.)  broad.  On  one  side  paste  a  piece  of  paper,  in  which  a  circu- 
lar hole  has  been  cut.  On 
this  clear  circular  space, 
draw  two  ink-marks  at 
right  angles  to  each 
other,  as  shown  in  Fig. 
292.  Fill  the  bottle  with 
clear  water  up  to  the 
level  of  the  horizontal 
ink-mark.  Hold  it  so 
that  a  horizontal  sun- 
beam from  the  heliostat 
may  pass  through  the 
clear  sides  of  the  bottle 
above  the  water,  and  no- 
tice that  the  beam  passes 
through  the  bottle  in  a 
straight  line.  Raise  the 
bottle  so  that  the  beam 
shall  pass  through  the 
water,  and  notice  that  the 
beam  is  still  straight.  FlG-  292- 

In  a  card,  cut  a  slit  about 

5  em.  long  and  1  mm.  wide.     Place  the  card  against  the  bottle  as 
shown  in  the  figure.    Reflect  the  beam  through  this  slit  so  that  it 


394  REFRACTION  OF  LIGHT. 

shall  fall  upon  the  surface  of  the  water  at  t,  the  intersection  of  the 
two  ink-marks.  Notice  that  the  reflected  beam  is  straight  until  it 
reaches  the  water,  but  that  it  is  bent  as  it  obliquely  enters  the 
water. 

612.  Refraction. — Refraction  of  light  is   the 
bending  of  a  luminous  ray  when  it  passes  from 
one  medium  to  another. 

613.  Index  of  Refraction. — If  a  ray  of  light  from 
L  (Fig.  293)  fall  upon  the  surface  of  water  at  A,  it  will  be 
refracted  as  shown  in  the  figure.    The  angle  LAB  is  the 
angle  of  incidence  and  KAC  the  angle  of  refraction,  BC 
being  perpendicular  to  the  water's  surface.     From  A  as  a 

centre,  with  a  radius  equal  to  unity, 
describe  a  circle.  From  the  points  m 
and  p,  where  this  circle  cuts  the  inci- 
dent and  refracted  rays,  draw  mn  and 
pq  perpendicular  to  BC.  Then  will 
mn  be  the  sine  of  the  angle  of  incidence 
and  pq  the  sine  of  the  angle  of  refrac- 
tion. The  quotient  arising  from 
dividing  the  sine  of  the  angle  of 
incidence  by  the  sine  of  the  angle  of  refraction  is 
called  the  index  of  refraction  for  the  two  media. 
It  is  evident  that  the  greater  the  refractive  power  of  the 
substance,  the  less  the  value  of  the  divisor  pq,  and  the 
greater  the  value  of  the  quotient,  the  index  of  refrac- 
tion. 

(a.)  The  following  table  gives  the  indices  of  refraction  when  light 
passes  from  a  vacuum  into  any  of  the  substances  named  : 


Air 1.000294 

Water 1.336 

Alcohol 1.374 

Crown  glass 1.534 


Flint  glass 1.575 

Carbon  bisulphide 1.678 

Diamond 2.439 

Lead  chromate 2.974 


REFRACTION  OF  LIGHT. 


395 


The  index  of  refraction  for  any  two  media  may  be  found  by  divid- 
ing the  absolute  index  of  one,  as  given  above,  by  the  absolute  index 
of  the  other. 

614.  Laws  of  Refraction  of  Light.— (1.) 
When  light  passes  perpendicularly  from  one  me- 
dium to  another  it  is  not  refracted. 

(2.)  When  light  passes  obliquely  from  a  rarer  to 
a  denser  medium  it  is  refracted  toward  a  line  drawn,  at 
the  point  of  incidence,  perpendicular  to  the  refracting 
surface*  or,  more  briefly,  it  is  refracted  toward  the 
perpendicular. 

(3.)  W^^en  light  passes  obliquely  from  a  denser 
to  a  rarer  medium,  it  is  refracted  from  the  per- 
pendicular. 

(4.)  The  incident  and  refracted  rays  are  in  the  same 
plane  which  is  perpendicular  to  the  refracting  surface. 

(5.)  The  index  of  refraction  is  constant  for  the  same  two 
media. 

615.  Illustrations  of  Refraction.— Put  a  small  coin  into 
a  tin  cup  and  place  the 
cup  so  that  its  edge  just 
intercepts  the  view  of 
the  coin.  A  ray  of  light 
coming  from  the  coin 
toward  the  observer 
must  pass  above  his  eye 
and  thus  be  lost  to 
sight.  If,  now,  water  be 
gradually  poured  into 
the  cup,  the  coin  will 
become  visible.  The 
rays  are  bent  down  as 
they  emerge  from  the 
water  and  some  of  them 
enter  the  eye.  For  the 

same  reason,  an  oar  or  other  stick  half  immersed  in  water  seems 
bent  at  the  water's  surface,  while  rivers  and  ponds  whose  bottoms 


FIG.  294. 


396 


REFRACTION  OF  LIGHT. 


are  visible  are  generally  deeper  than  they  seem  to  be.  (Fig.  294.) 
As  air  expands,  its  index  of  refraction  becomes  less.  Hence  the 
indistinctness  and  apparent  unsteadiness  of  objects  seen  through 
air  rising  from  the  surface  of  a  hot  stove.  Light  is  refracted  as  it 
enters  the  earth's  atmosphere.  Hence  the  heavenly  bodies  appear 
to  be  further  above  the  horizon  than  they  really  are  except  when 
they  are  overhead. 

616.  Total  Reflection.— When  a  ray  of  light 
passes  from  a  rarer  into  a  denser  medium,  it  may  always 
approach  the  perpendicular  so  as  to  make  the  angle  of  re- 
fraction less  than  the  angle  of  incidence  (§  614  [2]).  But 
when  a  ray  of  light  attempts  to  pass  from  a  denser  into  a 
rarer  medium  there  are  conditions 
under  which  the  angle  of  refraction 
cannot  be  greater  than  the  angle  of 
incidence.  Under  such  circum- 
stances the  ray  cannot  emerge 
from  the  denser  medium,  but 
mill  be  wholly  reflected  at  the 
point  of  incidence.  Fig.  295  represents  luminous  rays 
emitted  from  A,  under  water,  and  seeking  a  passage  into 
air.  Passing  from  the  perpendicular,  the  angle  of  refrac- 
tion increases  more  rapidly  than  the  angle  of  incidence 
until  one  ray  is  found  that  emerges  and  grazes  the  surface 
of  the  water.  Rays  beyond 
this  cannot  emerge  at  all. 


617.  The  Critical  An- 
gle. —  Imagine  a  spherical 
(Florence)  flask  half  filled 
with  water.  A  ray  of  light 
from  L  will  be  refracted  at  A 
in  the  direction  of  R.  If  the 
angle  of  incidence,  CAL}  be 


FIG.  295. 


FIG.  296. 


REFRACTION  OF  LIGHT. 


397 


gradually  increased  the  angle  of  refraction  will  be  gradually 
increased  until  it  becomes  90°,  when  the  ray  will  graze  the 
surface  of  the  water  AM.  If  the  source  of  light  be  still 
further  removed  from  (7,  as  to  ?,  the  ray  will  be  reflected 
to  r  (§  591).  For  all  media  there  is  an  incident  angle  of 
this  kind,  called  the  critical  or  limiting  angle,  beyond 
which  total  internal  reflection  will  take  the  place  of  refrac- 
tion. The  reflection  is  called  total  because  all  of  the 
incident  light  is  reflected,  which  is  never  the  case  in 
ordinary  reflection.  Hence,  a  surface  at  which  total  re- 
flection takes  place  constitutes  the  most  perfect  mirror 
possible.  The  critical  angle  (with  reference  to  air)  is 
48°  35'  for  water;  40°  49'  for  glass;  23°  43'  for  diamond. 

(a.)  From  this  it  follows,  as  may  be  seen  by  referring  to  Fig.  295, 
that  to  an  eye  placed  under  water,  all  visible  objects  above  the 
water  would  appear  within  an  angle  of  97°  10',  or  twice  the  critical 
angle  for  water. 

(6.)  The  phenomena  of  total  reflection  may  be  produced  by  placing 
the  bottle  shown  in  Fig.  292  upon  several  books  resting  upon  a  table, 
and  inverting  the  card  so  that  a  beam  of  light  reflected  obliquely 
upward  from  a  mirror  on  the  table  may  enter  through  the  slit  near 
the  bottom  of  the  bottle,  taking  a  direction  through  the  water  simi- 
lar to  the  line  IA  of  Fig.  296.  When  one  looks  into  an  aquarium  in 
a  direction  similar  to  rA,  images  of  fish  or  turtles  near  the  surface 
of  the  water  are  often  seen. 

(c.)  Place  a  strip  of  printed  paper  in  a  test-tube ;  hold  it  ob- 
liquely in  a  tumbler  of  water  and  look  downward  at  the  printing 
which  will  be  plainly  visible.  Change  the  tube  gradually  to  a 
vertical  position,  and  soon  the  part  of  the  tube  in  the  water  takes  a 
silvered  appearance  and  the  printing  becomes  invisible.  Show  that, 
in  this  case,  the  disappearance  of  the 
reading  is  due  to  total  reflection.  By 
dissolving  a  small  bit  of  potassium  bi- 
chromate in  the  water,  the  tube  will 
have  a  golden  instead  of  a  silver-like 
appearance. 

(d.)  Fig.  297  represents  a  glass  vessel 
partly  filled  with   water.      Mirrors    are  FIG.  297. 


398 


REFRACTION  OF  LIGHT. 


placed  at  m  and  n.     In  this  way  a  ray  may  be  reflected  at  m,  n  and  o, 
and  refracted  at  i. 

(e.)  Fig.  298  represents  a  glass  jar  with  an  opening,  from  which 

a  stream  of  water  issues  under  a 
head  (§  254  [a])  kept  constant. 
Through  a  lens  placed  opposite 
this  orifice,  a  concentrated  beam 
of  light  from  the  heliostat  is 
thrown  into  the  stream  of  water 
as  it  issues.  Internal  reflection 
keeps  most  of  it  there,  a  prisoner. 
The  stream  of  water  is  full  of 
light  and  appears  a  stream  of 
melted  metal.  Thrust  a  finger 
into  the  stream  and  notice  the 
effect.  Place  a  piece  of  red  glass 
between  the  heliostat  and  the 
lens  ;  the  water  looks  like  blood. 
Thrust  the  finger  into  the  stream  again.  Repeat  the  experiment 
with  pieces  of  glass  of  other  colors  in  place  of  the  red. 


FIG.  298. 


618.  Refraction  Explained. — To  understand  the 
way  in  which  a  ray  of  light  is  refracted,  let  us  consider  its 
passage  through  a  glass  prism,  ABC.  It  must  be  under- 
stood that  the  velocity  of  light  is 
less  in  glass  than  in  air,  and 
that  the  direction  in  which  a 
wave  moves  is  perpendicular  to 
its  wave  front.  A  wave  in  the 
ether  approaches  the  surface  of  the 
prism  AB.  When  at  a,  the  lower  end  of  the  wave  front 
first  strikes  the  glass  and  enters  it.  The  progress  of  this 
end  of  the  wave  front,  being  slower  than  that  of  the  other 
which  is  still  in  the  air,  is  continually  retarded  until  the 
whole  front  has  entered  the  glass.  The  wave  front  thus 
assumes  the  position  shown  at  c.  But  the  path  of  the 
wave  being  perpendicular  to  the  front  of  the  wave,  this 


FIG.  299. 


REFRACTION  OF  LIGHT.  399 

change  of  front  causes  a  change  in  the  direction  of  the  ray 
which  is  thus  refracted  toward  a  perpendicular.  The  wave 
now  moves  forward  in  a  straight  line  until  the  top  of  the 
wave  front  strikes  A  C,  the  surface  of  the  prism,  as  shown 
at  m.  The  upper  end  of  the  wave  front  emerging  first 
into  the  air  gains  upon  the  other  end  of  the  front  which  is 
still  moving  more  slowly  in  the  glass.  When  the  lower 
end  emerges  from  the  glass,  the  wave  has  the  position 
shown  at  n.  This  second  change  of  front  involves  another 
change  in  the  direction  of  the  ray  which  is  now  refracted 
from  the  perpendicular. 

619.  Three  Kinds  of  Refractors.—  When  a  ray 

of  light  passes  through  a  refracting  medium,  three  cases 
may  arise  : 

(I.)  When  the  refractor  is  bounded  by  planes,  the  re- 
fracting surfaces  being  parallel. 

(2.)  When  the  refractor  is  bounded  by  planes,  the  re- 
fracting surfaces  being  not  parallel.  The  refractor  is  then 
called  a  prism. 

(3.)  When  the  refractor  is  bounded  by  two  surfaces  of 
which  at   least    one   is 
curved.     The  refractor 
is  then  called  a  lens. 


62O.  Parallel 
Plates.  —  When  a  ray 
passes  through  a  me- 

dium bounded  bv  paral- 

111         j.u       iL    L- 
lei  planes  the  refractions 

at  the  two  surfaces  are  equal  and  contrary  in  direction. 
The  direction  of  the  ray  after  passing  through  the  plate  is 


400 


REFRACTION  OF  LIGHT. 


parallel  to  its  direction  before  entering;  the  ray  merely 
suffers  lateral  aberration.  Objects  seen  obliquely  through 
such  plates  appear  slightly  displaced  from  their  true  position. 

621.  Prisms. — A  prism  produces  two  simultaneous 
effects  upon  light  passing  through  it;  a  change  of  direc- 
tion and  decomposition.  The  second  of  these  effects  will 
be  considered  under  the  head  of  dispersion  (§  636). 

(a.)  Let  mno  represent  a  section  formed  by  cutting  a  prism  by  a 
plane  perpendicular  to  its  edges.  A  ray  of  light  from  L  being  re- 
fracted at  a  and  b  en- 
ters the  eye  in  the  di- 
rection Ic.  The  object 
being  seen  in  the  direc- 
tion of  the  ray  as  it 
enters  the  eye  (§  594), 
appears  to  be  at  r.  An 
object  seen  through  a 
prism  seems  to  be 
moved  in  the  direction 
of  the  edge  that  sepa- 
rates the  refracting 
surfaces.  The  rays  FIG.  301. 

themselves     are    bent 

toward  the  side  that  separates  the  refracting  surfaces,  or  toward 
the  thickest  part  of  the  prism. 

(6.)  Prisms  are  generally  made  of  glass,  their  principal  sections 
being  equilateral  triangles.  In  order  to  give  a 
liquid  the  form  of  a  prism,  it  is  placed  in  a 
vessel  (Fig.  302)  in  which  at  least  two  sides 
are  glass  plates  not  parallel.  Bottles  are  made 
for  this  purpose. 

(c.}  In  Fig.  303,  ABC  is  the  principal  section 
of  a  right-angled  isosceles,  glass 
prism,  right-angled  at  C.     A  ray 
of  light  falling  perpendicularly 
upon  either  of  the  cathetal  (cathetus)  surfaces,  as  AC, 
will  not  be  refracted.     With  AB,  it  will  make  an 
angle  of  45°  which  exceeds  the  critical   angle   for 
glass  (§  617).     It  will  therefore  be  totally  reflected 
and  pass  without  refraction  from  the  cathetal  surface  BC.     Such 
prisms  are  often  used  in  optics  instead  of  mirrors. 


FIG.  302. 


REFRACTION  OF  LIGHT. 


401 


622.  Lenses.— Lenses  are  generally  made  of  crown 
glass  which  is  free  from  lead,  or  of  flint  glass  which  con- 
tains lead  and  has  greater  refractive  power.  The  curved 
surfaces  are  generally  spherical.  With  respect  to  their 
shape,  lenses  are  of  six  kinds: 
123 


Thinner  at  the  middle  than 
at  the  edges. 


FIG.  304. 

(1.)  Double-convex,  1  Thicker  at  tlie  middle  than 

(2.)  Plano-convex,  at  the  ed 

(3.)  Concavo-convex,  or  meniscus,  J 

The  double-convex  may  be  taken  as  the  type  of  these. 

(4.)  Double-concave,  ~\ 

(5.)  Plano-concave,  I 

(6.)  Convex-concave,  or  diverging  \ 
meniscus,  J 

The  double  concave  may  be  taken  as  the  type  of  these. 
(a.)  The  effect  of  convex  lenses  may  be  considered  as  produced  by 
two  prisms  with  their  bases  in  contact  ;  that  of  concave  lenses,  by 
two  prisms  with  their  edges  in  contact. 

623.  Centre  of  Curvature  ;  Principal  Axis  ; 
Optical  Centre.  —  A  double-convex  lens  may  be  de- 
scribed as  the  part  common  to  two  spheres  which  intersect 
each  other.  The  centres  of  these  spheres  are  the  centres 
of  curvature  of  the  lens.  The  straight  line  passing 
through  the  centres  of  curvature  is  the  principal  axis  of 
the  lens.  In  every  lens  there  is  a  point  on  the  principal 
axis  called  the  optical  centre.  When  the  lens  is  bounded 
by  spherical  surfaces  of  equal  curvature,  as  is  generally  the 
case,  the  optical  centre  is  at  equal  distances  from  the  two 


402  REFRACTION  OF  LIGHT. 

faces  of  the  lens.  Any  straight  line,  other  than  the  prin- 
cipal axis,  passing  through  the  optical  centre  is  a  second- 
ary axis. 

(a.)  If  a  ray  of  light  passing  through  the  optical  centre  be  re- 
fracted at  all,  the  two  refractions  will  be  equal  and  opposite  in  direc- 
tion. The  slight  lateral  aberration  thus  produced  may  be  disregarded. 

624.  Principal  Focus. — All  rays  parallel  to 
the  principal  axis  will,  after  two  refractions,  con- 
verge at  a  point  called  the  principal  focus.  This 
point  may  lie  on  either  side  of  the  lens,  according  to  the 
direction  in  which  the  light  moves;  it  is  a  real  focus.  The 
greater  the  refracting  power  of  the  substance  of  which  the 


FIG.  305. 

(ens  is  made,  the  nearer  the  principal  focus  will  be  to  the 
lens.  In  a  double-convex  lens  of  crown  glass,  the  principal 
focal  distance  is  equal  to  the  radius  of  curvature;  in  a 
plano-convex  lens  of  the  same  material,  it  is  twice  as  great. 

(a.)  The  position  of  the  principal  focus  of  a  lens  is  easily  deter- 
mined. Hold  the  lens  facing  the  sun.  The  parallel  solar  rays 
incident  upon  the  lens  will  converge  at  the  principal  focus.  Find 
this  point  by  moving  a  sheet  of  paper  back  and  forth  behind  the 
lens  until  the  bright  spot  formed  upon  the  paper  is  brightest  and 
smallest. 

(&.)  It  is  also  true  that  rays  diverging  from  a  point  at  twice  the 
principal  focal  distance  from  the  lens  will  converge  at  a  point  just 
as  far  distant  on  the  other  side  of  the  lens.  Rays  diverging  from 
/  will  converge  at  /',  these  two  points  being  at  twice  the  focal  dis- 
tance from  the  lens.  By  experimenting  with  a  lens  and  candle- 
flame  until  the  flame  and  its  image  are  at  equal  distances  from  the 
lens,  we  are  able,  in  a  second  way,  to  determine  the  principal  focal 
distance  of  the  lens.  The  conjugate  foci  situated  at  twice  the  prin- 
cipal focal  distance  are  called  secondary  foci. 


REFRACTION  OF  LIGHT.  403 

625.  Conjugate  Foci. — Eays  diverging  from  a 
luminous  point  in  the  principal  axis  at  a  small  distance 
beyond  the  principal  focus  on  either  side  of  the  lens  will 
form  a  focus  on  the  principal  axis  beyond  the  other  prin- 
cipal focus.  Thus,  rays  from  L  will  converge  at  /;  con- 
versely, rays  from  I  will  converge  at  L  (§  602).  If  the 
luminous  point  be  in  a  secondary  axis,  the  rays  will  con- 
verge to  a  point  in  the  same  secondary  axis.  Two 


FIG.  306. 

points  thus  related  to  each  other  are  called  con- 
jugate foci;  the  line  joining  them  always  passes 
through  the  optical  centre. 

(a.)  If  the  luminous  point  be  more  than  twice  the  focal  distance 
from  the  lens,  the  conjugate  focus  will  lie  on  the  other  side  of  the 
lens  at  a  distance  greater  than  the  focal  distance,  but  less  than  twice 
the  focal  distance.  If  the  luminous  point  be  moved  toward  the 
lens,  the  focus  will  recede  from  the  lens.  When  the  luminous 
point  is  at  one  secondary  focus,  the  rays  will  converge  at  the  other 
secondary  focus.  When  the  luminous  point  is  between  the  second- 
ary and  principal  foci,  the  rays  will  converge  beyond  the  secondary 
focus  on  the  other  side  of.the  lens.  Wrhen  the  luminous  point  is  at 
the  focal  distance,  the  emergent  rays  will  be  parallel  and  no  focus 
will  be  formed.  When  the  luminous  point  is  at  less  than  the  focal 
distance,  the  emergent  rays  will  still  diverge  as  if  from  a  point  on 
the  same  side  of  the  lens,  more  distant  than  the  principal  focus. 


404 


REFRACTION  OF  LIGHT. 


FIG.  307. 

This  focus  will  be  virtual.  Conversely,  converging  rays  falling 
upon  a  convex  lens  will  form  a  focus  nearer  the  lens  than  the 
principal  focus.  (See  Fig.  307.) 

626.    Conjugate   Foci  of  Concave  Lens.— 

Rays  from  a  luminous  point  at  any  distance  whatever  will 
be  made  more  divergent  by  passing  through  a  concave  lens. 


FIG.  308. 

Rays  parallel  to  the  principal  axis  will  diverge  after  refrac- 
tion as  if  they  proceeded  from  the  principal  focus.  In 
any  case,  the  focus  will  be  virtual,  and  nearer  the  lens  than 
the  luminous  point. 

627.  Images  Formed  by  Convex  Lenses.— 

The  analogies  between  the  convex  leris  and  the  concave 


REFRACTION  OF  LIGHT,  405 

mirror  cannot  have  escaped  the  notice  of  the  thoughtful 
pupil.  Others  will  appear.  If  secondary  axes  be  nearly 
parallel  to  the  principal  axis,  well-defined  foci  may  be 
formed  upon  them,  as  well  as  upon  the  principal  axis.  A 
number  of  these  foci  may  determine  the  position  of  an 
image  formed  by  a  lens. 

(a.)  The  linear  dimensions  of  object  and  image  are  directly  as 
their  respective  distances  from  the  centre  of  the  lens  ;  they  will  be 
virtual  or  real,  erect  or  inverted,  according  as  they  are  on  the  same 
side  of  the  lens  or  on  opposite  sides. 

628.  Construction  for  Real  Images.— To  determine 
the  position  of  the  image  of  the  object  AB  (Fig.  309),  draw  from 
any  point,  as  A,  a  line  parallel  to  the  principal  axis.  After  refrac- 


FIG.  309. 

tion,  the  ray  represented  by  this  line  will  pass  through  F,  the  prin- 
cipal focus.  Draw  the  secondary  axis  for  the  point  A.  The  inter- 
section of  these  two  lines  at  a  determines  the  position  of  the  con- 
jugate focus  of  A.  In  similar  manner,  the  conjugate  focus  of  B  is 
found  to  be  at  &.  Joining  these  points,  the  line  ab  is  the  image  of 

the  line  AB. 

. 

629.  Diminished  Real  Image.— If  the  object 
be  more  than  twice  the -focal  distance  from  the  convex 
lens,  its  image  will  be  real,  smaller  than  the  object  and 
inverted  (Fig.  310).  Construct  the  image  as  indicated  in 
the  last  paragraph. 


REFRACTION  OP  LIGHT. 


FIG.  310. 

63O.   Magnified  Real  Image.— If  the  object  be 
further  from  the  lens  than  the  principal  focus,  but  at  a 


FIG.  311. 

distance  less  than  twice  the  focal  distance,  the  image  will 
be  real,  magnified  and  inverted.  (Fig.  311.)  Construct 
the  image. 


REFRACTION  OF  LIGHT.  40? 

631.  Virtual   Image.— If   the  object   be  placed 
nearer  the  lens  than  the  principal  focus,  the  image  will  be 
virtual,  magnified  and  erect.     (Fig.  312.)     This  explains 
the  familiar  magnifying  effects  of  convex  lenses.     Con- 
struct the  image. 

632.  Image  of  Concave  Lens. — Images  formed 
by  a  concave  lens  are  virtual,  smaller  than  the  object  and 
erect.    The  construction  of  the  image  is  shown  in  Fig. 
313. 


FIG.  313. 

Note. — The  power  of  the  convex  lens  to  form  real  and  diminished 
images  of  distant  objects  and  magnified  images  of  near  objects,  is 
of  frequent  application  in  such  optical  instruments  as  the  micro- 
scope, telescope,  magic  lantern,  lighthouse  lamps,  etc.  Owing  to 
the  identity  between  heat  and  luminous  rays,  a  convex  lens  is  also 
a  "  burning-glass." 

633.  Spherical  Aberration. — The  rays  that  pass 
through  a  spherical  lens  near  its  edge  are  more  refracted 
than  those  that  pass  nearer  the  centre.  They,  therefore, 
converge  nearer  the  lens.  A  spherical  lens  cannot  refract 
all  of  the  incident  rays  to  the  same  point.  Hence 
"spherical  aberration"  and  its  annoying  consequences  in 
the  construction  and  use  of  optical  apparatus. 


408  REFRACTION  OF  LIGHT. 


EXERCISES. 

1.  («.)  What  is  refraction  of  light  ?    (&.)  State  the  laws  governing 
the  same,  and  (c.)  give  an  illustrative  diagram. 

2.  (a.)  Name  and  illustrate  by  diagram  the  different  classes  of 
lenses.    (&.)  Explain,  with  diagram,  the  action  of  the  burning-glass. 

3.  (a.)  Explain  the  cause  of   total  reflection.     (6.)   Show,    with 
diagram,  how  the  secondary  axes  of  a  lens  mark  the  limits  of  the 
image. 

4.  (a.)  Using  a  convex  lens,  what  must  be  the  position  of  an 
object  in  order  that  its  image  shall  be  real,  magnified,  and  inverted  ? 
(b.)  Same,  using  a  concave  lens  ? 

5.  (a.)  Show  how  a  ray  of  light  may  be  bent  at  a  right  angle  by 
a  glass  prism.     (6.)  The  focal  distance  of  a  convex  lens  being  6 
inches,  determine  the  position  of  the  conjugate  focus  of  a  point 
12  inches  from  the  lens,    (c.)  18  inches  from  the  lens. 

6.  (a.)  The  focal  distance  of  a  convex  lens  is  30-c/ra.     Find  the 
conjugate  focus  for  a  point  15  cm.  from  the  lens.     (6.)  How  may  the 
focal  length  of  a  lens  be  determined  experimentally  ? 

7.  If  an  object  be  placed  at  twice  the  focal  distance  of  a  convex 
lens,  how  will  the  length  of  the  image  compare  with  the  length  of 
the  object? 

8.  A  small  object  is  12  inches  from  a  lens  ;  the  image  is  24  inches 
from  the  lens  and  on  the  opposite  side.    Determine  (by  construction) 
the  focal  distance  of  the  lens. 

9.  A  candle  flame  is  6  feet  frpm  a  wall ;  a  lens  is  between  the 
flame  and  the  wall,  5  feet  from  the  latter.     A  distinct  image  of  the 
flame  is  formed  upon  the  wall,    (a.)  In  what  other  position  may 
the  lens  be  placed,  that  a  distinct  image  may  be  formed  upon  the 
wall  ?    (&.)  How  will  the  lengths  of  the  images  compare  ? 


Recapitulation. — In  this  section  we  have  considered 
the  Definition,  Index,  Laws  and  Explanation 
of  refraction ;  Internal  Reflection ;  Plates, 
Prisms  and  Lenses ;  principal  and  conjugate  Foci 
of  lenses ;  Construction  for  conjugate  foci  and 
images;  Spherical  Aberration. 


CHR  OMA  TICS—  SPECTRA.  409 


ECTfON    IV. 


CHROMATICS.— SPECTRA. 

634.  Other  Results  of  Refraction. — In  our  previous 
consideration  of  luminous  rays  we  have  studied  the  effect  of  reflec- 
tion and  refraction  upon  the  direction  of  rays ;  in  fact,  we  have 
dealt  with  only  those  properties  which  are  common  to  all  luminous 
rays.  But  the  properties  of  light  and  the  phenomena  of  refraction 
are  not  so  simple  as  we  might  thus  be  led  to  suppose.  Most 
luminous  objects  emit  light  of  several  kinds  blended  together.  We 
must  not  be  satisfied  with  our  knowledge  of  light  until  we  are  able 
to  sift  these  varieties  one  from  the  other,  and  to  deal  with  any  one 
kind  by  itself. 


FIG.  314. 

635.  Solar  Spectrum. — Admit  a  sunbeam  through 
a  very  small  opening  in  the  shutter  of  a  darkened  room. 
The  opening  may  be  prepared  by  cutting  a  slit  an  inch 
(25  mm.)  long  and  ^g-  of  an  inch  (1  mm.)  wide  in  a  card. 
See  that  the  edges  of  the  slit  are  smooth.  Tack  the  slit 
over  a  larger  opening  in  the  shutter.  If  we  look  at  the 
aperture  from  E  we  shall  see  the  sun  beyond.  The  path 
of  the  beam  from  S  to  E  is  made  visible  by  the  floating 
18 


410  CHROMATICS— SPECTRA. 

dust.  If  a  prism  be  placed  in  the  path  of  the  beam,  as 
shown  in  Fig.  314,  the  sides  of  the  slit  and  edges  of  the 
prism  being  horizontal,  the  beam  will  be  refracted  upward. 
If  the  refracted  beam  be  caught  upon  a  screen,  it  will 
appear  as  a  band  of  differently  colored  light,  passing  by 
imperceptible  gradations  from  red  at  the  bottom,  through 
orange,  yellow,  green,  blue  and  indigo  to  violet  at  the 
upper  end  of  the  beautifully  colored  band.  This  colored 
band  is  called  the  solar  spectrum. 

(a.)  The  different  colors  do  not  occupy  equal  space  in  the  spectrum, 
orange  having  the  least  and  violet  the  most.  The  initials  of  these 
colors  form  the  meaningless  word  VIBGYOR,  which  may  aid  the 
memory  in  remembering  these  prismatic  colors  in  their  proper 
order.  By  placing  the  slit  in  a  vertical  position,  and  standing  the 
prism  on  its  end  so  that  its  edges  will  be  parallel  with  the  sides  of 
the  slit,  the  spectrum  will  be  projected  as  a  horizontal  band. 

636.  Dispersion.— By  looking  at  Fig.  314,  it  will 
be  seen  that  the  red  rays  have  been  refracted  the  least  and 
the  violet  the  most  of  all  the  luminous  rays.     This  sepa- 
ration of  the  differently  colored  rays  by  the  prism 
is  called  the  dispersion  of  light ;  it  depends  upon  the 
fact  that  rays  of  different  colors  are  refracted  in  different 
degrees. 

637.  Pure  Spectrum. — The  spectrum  above  de- 
scribed is  composed  of  overlapping  and  differently-colored 
images  of  the  slit.     In  a  pure  spectrum  these  images  must 
not  overlap.    The  first  requisite  in  preventing  this  over- 
lapping is  that  the  slit  be  very  narrow. 

(a.)  The  most  simple  way  of  producing  a  pure  spectrum  is  to  look 
through  a  prism  at  a  very  narrow  slit  in  the  shutter  of  a  darkened 
room.  The  edges  of  the  prism  should  be  parallel  to  the  slit ;  the 
prison  should  be  at  least  five  feet  (1£  m.)  from  the  slit ;  the  prism 
should  be  turned  until  the  colored  image  of  the  slit  is  et  the  least 


CHROMATICS — SPECTRA.  411 

angular  distance  from  the  slit  itself.  A  pure  spectrum  is  also 
obtained  by  passing  the  beam  through  several  prisms  in  succession, 
thus  increasing  the  dispersion. 

638.  Fraunhofer's  Lines. — A  pure  solar  spectrum 
is  not  continuous,  but  is  crossed  by  numerous  dark  lines, 
many  hundreds  of  which  have  been  counted  and  accu- 
rately mapped.  The  more  conspicuous  of  these  dark  lines 
are  distinguished  by  letters  of  the  alphabet,  as  shown  in 
Fig.  315.  Each  of  these  dark  lines  indicates  that  a  par- 
ticular kind  of  ray  is  wanting  in  solar  light. 

AaBCD  E6P  G  HH' 


ROY  G  B  I  V 

FIG.  315. 

(a.)  The  spectra  of  incandescent  solids  are  continuous,  from  the 
extreme  red  to  a  limit  depending  upon  the  temperature.  The 
spectra  of  incandescent  gases  (not  containing  solid  particles  in 
suspension)  are  non-continuous,  consisting  of  a  number  of  definite 
bright  lines.  A  candle  or  gas  flame  gives  a  continuous  spectrum 
because  it  is  chiefly  due  to  the  incandescence  of  solid  carbon 
particles. 

(&.)  The  spectroscope  is  an  instrument  for  producing  and  observing 
pure  spectra.  It  has  proved  to  be  one  of  the  most  powerful  aids 
to  modern  science.  It  affords  the  most  delicate  means  of  chemical 
analysis ;  by  its  aid  several  elements  have  been  discovered ;  the 
presence  of  7TTF^.Tnnr  of  a  grain  of  sodium  has  been  detected  by 
"spectrum  analysis."  It  is  of  incalculable  importance  to  the 
astronomer.  For  definite  information,  the  pupil  is  necessarily 
referred  to  some  of  the  excellent  manuals  upon  the  subject  recently 
published. 

639.  Synthesis  of  White  Light.— By  analysis, 
we  have  shown  that  white  light  is  composed  of  seven 
primary  colors.  The  same  fact  may  be  shown  synthetically, 
for  by  recombining  these  spectrum  colors  white  light  will 
be  produced. 


CHROMATICS. 


FIG.  316. 

(«.)  This  recombination  may  be  effected  by  means  of  a  convex 
lens  (Fig.^316)  or  a  concave  mirror.  Another  simple  method  of 
recombination  is  afforded  by  "  Newton's  disc  " 
(Fig.  317),  which  contains  the  prismatic  colors 
in  proper  proportion.  When  this  disc  is  rapidly 
revolved  by  means  of  the  whirling  table  (see 
Fig.  7),  or  by  fastening  it  to  a  large  top,  the 
colors  are  blended  and  the  disc  appears  grayish 
white.  Still  another  way  of  producing  this 
recomposition  is  to  pass  the  light  as  it  emerges 
from  the  first  prism  through  a  second  prism, 
placed  in  a  position  inverted  with  reference  to  the  first. 


FIG.  317. 


64O.  Color  of  Bodies.— The  color  of  a  body  is  its 
property  of  reflecting  or  transmitting  to  the  eye  light  of 
that  particular  color,  the  other  rays  being  absorbed.  This 
power  may  be  described  as  selective  absorption. 

(a.)  Properly  speaking,  color  is  not  a  property  of  matter,  but  of 
light.  A  ribbon  is  called  red,  but  the  redness  belongs  to  the  light, 
not  to  the  ribbon.  There  would  be  more  propriety  in  saying  that 
the  ribbon  has  all  the  other  colors  of  the  rainbow,  because  it  absorbs 
the  others  and  reflects  the  red.  If  the  red  ribbon  be  placed  in  the 
green  or  blue  of  the  spectrum  it  will  appear  black  because  it 
receives  no  red  rays  to  reflect.  Colored  substances  decompose  the 
incident  light,  absorbing  some  rays  and  assuming  the  hue  of  those 
they  reflect  or  transmit  to  the  eye.  A  body  that  absorbs  very  few 
of  the  rays  is  white  ;  one  that  absorbs  nearly  all  is  black.  There- 
fore, black  is  not  a  color  but  its  absence. 


THE  RAINBOW.  413 

(6.)  Paint  three  narrow  strips  of  cardboard,  one  vermilion  red, 
one  emerald  green,  and  the  other  aniline  violet.  Be  sure  that  the 
coats  are  thick  enough  thoroughly  to  hide  the  cardboard.  When 
dry,  hold  the  red  strip  in  the  red  of  the  solar  spectrum  ;  it  appears 
red.  Move  it  slowly  through  the  orange  and  yellow  ;  it  grows 
gradually  darker.  In  the  green  and  colors  beyond,  it  appears  black. 
Repeat  the  experiment  with  the  other  two  strips,  and  carefully 
notice  that  the  effects  are  in  accordance  with  the  principle  above 
stated. 

641.  The  Rainbow. — The  rainbow  is  due  to  re- 
fraction, reflection  and  dispersion  of  sunlight  by  water- 
drops.  The  necessary  conditions  are  : 

(1.)  A  shower  during  sunshine. 

(2.)  That  the  observer  shall  stand  with  his  back  to  the 
sun,  between  the  falling  drops  and  the  sun. 

(a.)  The  centre  of  the  circle  of  which  the  rainbow  forms  a  part 
is  in  the  prolongation  of  a  line  drawn  from  the  sun  through  the 
eye  of  the  observer.  This  line  is  called  the  axis  of  the  bow. 


FIG.  318. 


642.  Dispersion  by  a  Raindrop. — Suppose  the 
circle  whose  centre  is  at  0  (Fig.  318)  to  represent  the  section 
of  a  raindrop.  A  ray  of  sunlight,  as  Sm,  falling  upon  the 
raindrop  would  be  refracted  at  m,  reflected  at  n,  and  again 


414:  THE  RAINBOW. 

refracted  at  m'.  In  passing  thus  through  the  drop,  the 
light  is  also  decomposed.  If  m'E  represent  the  path  of 
a  red  ray,  the  violet  ray  will  traverse  a  path  above,  because 
violet  is  refracted  more  than  red.  The  path  of  this  violet 
ray  may  be  represented  by  m'B.  If  the  raindrop  be  in  the 
exact  position  for  the  red  ray,  m'E,  to  enter  the  eye  of  the 
observer,  the  violet  and  other  colored  rays  will  pass  over* 
head  and  not  be  seen.  This  drop  will  appear  red. 

643.  Successive  Colors  of  the  Rainbow.— In  order 

that  a  violet  ray 
may  enter  the  eye 
at  E,  it  must  pro- 
ceed from  a  drop 
situated  below  the 
one  that  sends  the 
red  ray.  This  drop 
will  appear  violet. 
Intervening  drops 
will  give  the  inter- 
vening colors  of 
the  solar  spectrum 
in  their  proper  or- 
der as  is  shown  in 
Fig.  319.  Owing 
to  the  distance  of 
the  sun,  all  of  the 
incident  rays  are 
FIG.  310.  parallel  with  the 

axis    EO,    drawn 

from  the  sun  through  E,  the  eye  of  the  observer,  to  0,  the  centre 
of  the  circle  of  which  the  bow  forms  a  part.  The  angle  between 
the  incident  and  the  emergent  ray,  SRE,  and  consequently  the  angle 
REO,  is,  for  the  red  ray,  about  42°.  The  angles  S'  VE  and  VEO  are, 
for  the  violet  ray,  about  40°.  The  other  colors  lying  between  these, 
it  will  be  seen  that  the  angular  width  of  the  rainbow  is  about  two 
degrees. 

644.  Form  and  Extent  of  the  Rainbow.— 

From  Fig.  320,  it  will  be  seen  that  every  drop  in  the  arc  of 


THE  RAINBOW.  415 

a  circumference  drawn,  with  0  as  a  centre  and  with  0  V  as 
radius,  being  opposite  the  sun  and  having  the  same  angular 
distance  from  OE,  viz.,  40°,  will 
send  violet  colored  rays  to  the  eye 
at  E,  and  the  violet  colored  part  of  a» 
the  bow  will  be  a  circular  arch.  s'~ 
For  the  same  reason,  the  red  of  the  s 
bow  is  a  circular  arch  lying  without 


the  violet  and  at  an  angular  dis- 

tance of  two  degrees   therefrom; 

the  other  colors  will  form  circular 

arches  lying  between  these  two.  FIG.  320. 

If  the  sun  be  at  the  horizon,  EO 

will  be  horizontal  and  the  arches  will  be  semicircles.     If 

the  sun  be  above  the  horizon,  0  will  be  depressed  below 

the  horizon  and  less  than  semicircles  will  be  seen.     If  the 

observer  be  on  a  mountain-top  or  up  in  a  balloon,  he  may 

see  more  than  a  semicircle. 

645.  The  Secondary  Bow.  —  Sometimes  two  col- 
ored arches  are  seen,  one  within  the  other.  The  inner 
which  we  have  just  considered  is  called  the  primary  bow  ; 
the  outer,  the  secondary  bow. 

(a.)  In  explaining  the  primary  bow  we  traced  a  ray  of  light  fall- 
ing upon  the  top  of  the  raindrop  ;  to  explain  the  secondary  bow  we 
trace  a  ray  falling  upon  its  lower  part.  Such  a  ray,  as  8m,  will  be 
refracted  at  m,  reflected  at  n  and  n',  and  again  refracted  at  m', 
coming  to  the  eye  at  E.  If  the  ray  which  thus  comes  to  the  eye  at 
E  be  a  red  ray,  the  violet  will  follow  m'  V,  and  thus,  passing  below 
the  eye  because  of  its  greater  refrangibility,  be  lost  to  sight.  The 
drop  that  sends  a  violet  ray  to  the  eye  at  E  must  be  placed  abov$ 
instead  of  below  the  drop  that  sends  the  red  ray.  (Fig.  321  ) 

(5.)  In  the  secondary  bow,  the  red  arch  will  be  on  the  inside,  with 
an  angular  distance  from  the  axis  EO  of  about  51°,  while  the  violet 
will  be  on  the  outside  at  an  angular  distance  of  about  54°.  In  the 


416 


CHR  QMA  TICS— SPECTRA. 


FIG.  321. 

case  of  either  bow  some  light  is  lost  at  each  reflection  ;  therefore, 
since  there  are  more  reflections  in  the  secondary  bow,  this  will 
appear  fainter. 

646.  Chromatic  Aberration. — It  is  impossible, 
by  means  of  a  single  spherical  convex  lens,  to  bring  all  of 
the  incident  rays  to  a  common  focus.    The  blue  and  violet 

rays  being  refracted  more  than 
the  red  rays  will  converge  at 
points  nearer  the  lens.  In  con- 
sequence of  this,  when  an  image 
is  projected  upon  a  screen,  the 
image  is  surrounded  with  a  col- 
ored border,  the  color  depending  upon  the  distance  of  the 
screen  from  the  lens.  This  inability  of  a  single  lens 
to  bring  differently  colored  rays  to  the  same  focus 
is  called  chromatic  aberration. 

647.  Achromatic  Lens.— A  convex  lens  of  crown 
glass,  by  combination  with  a  concave  lens  of  flint  glass,  may 
have  its  dispersive  power  neutralized  without  completely 


FIG.  322. 


CUR  OMA  TICS— SPECTRA .  417 

neutralizing  its  refraction.  As  the  converging  effect  of  the 
compound  lens  is  not  destroyed,  images  may  be  formed ; 
as  the  dispersive  effect  is  destroyed,  the  colored  fringe  is 
avoided.  A  co^nbinatio1^  of  lenses  by  ivhich  disper- 
sion is  avoided  and  refraction  secured  is  called  an 
achromatic  lens. 

648.  Properties  of  the  Spectrum.— We  have  seen  that 
we  may  decompose  a  sunbeam  by  availing  ourselves  of  the  varymg 
refrangibility  of  the  different  kinds  of  rays  of  which  it  is  composed. 
We  have  been  able  in  this  manner  to  produce  the  seven  primary 
colors  from  white  light.     But  our  analytic  investigations  must  go 
still  further.    Beyond  the  limits  of  the  visible  spectrum,  in  both 
directions,  there  are  rays  that  do  not  excite  the  optic  nerve,  the  ex- 
istence of  which,  however,  may  be  easily  proved.     The  spectrum 
has  three  properties  which  we  must  consider  in  detail :  luminous, 
thermal  and  actinic. 

649.  Luminous  Spectrum. — We  have  seen  the 
difference  of  rays  in  different  parts  of  the  spectrum  in  re- 
gard to  color,  but  they  also  differ  in  respect  to  intensity  or 
illuminating  power.    An  object,  as  a  printed  page,  will  be 
illuminated  more  strongly,  and  therefore  seen  more  dis- 
tinctly, when  placed  in  the  yellow  than  when  placed  in  the 
red  or  violet  part  of  the  spectrum. 

(a  )  The  difference  in  color  between  the  rays  found  in  different 
parts  of  the  spectrum  is  merely  one  of  rate  of  vibration  or  wave- 
length. The  intensity  of  the  light  found  at  any  particular  part  of 
the  spectrum  depends  upon  the  amplitude  of  vibration.  In  respect 
to  the  visible  spectrum,  it  may  be  said  that  brightness  is  to  light 
what  loudness  is  to  sound  (§  431),  that  color  is  to  light  what  pitch 
is  to  sound  (§  434). 

(&.)  The  length  of  an  ether- wave  that  can  awaken  the  sensation  of 
redness  is  about  OTTO*  °f  an  *nch  >  °^  tliat  which  can  awaken  th« 
sensation  of  violet,  about  ^^in;*  The  waves  corresponding  to  the 
intermediate  colors  have  intermediate  lengths. 

650.  Thermal  Spectrum.  —  If  a  very  delicate 
thermometer  or  thermopile  be  successively  placed  in  vari- 


418  CHROMATICS— SPECTRA. 

ous  parts  of  the  spectrum  it  will  be  found  that  the  tem- 
perature is  scarcely  affected  in  the  violet,  but  that  there  is 
a  continual  increase  in  temperature  as  the  thermometer  is 
moved  toward  the  other  end  of  the  spectrum,  it  being  quite 
marked  in  the  red.  The  greatest  augmentation  of  tem- 
perature takes  place  beyond  the  red,  wholly  outside  the 
visible  spectrum.  We  thus  detect  ultra-red  rays  con- 
stituting a  heat  spectrum.  Their  position  indicates 
their  low  refrangibility  and  increased  wave-length.  Be- 
cause of  its  diathermancy,  a  rock-salt  prism  is  desirable  for 
this  experiment;  glass  absorbs  most  of  the  ultra-red  rays. 

651.  Actinic  Spectrum. — The  actinic  or  chemical 
effects  of  sunlight  are,  in  a  general  way,  familiar  to  all. 
For  example,  plants  absorb  carbon  from  the  atmosphere 
only  during  the  day  time.  Silver  chloride  is  very  sen- 
sitive to  this  action  of  sunlight.  The  sensitive  paper 
of  the  photographer  will  remain  unchanged  in  the 
dark  ;  it  will  be  quickly  blackened  in  the  light.  If  a 
piece  of  paper  freshly  washed  in  a  solution  of  sulphate  of 
quinine,  or  some  other  fluorescent  substance,  be  held  in  the 
ultra-violet  rays,  it  will  become  visible.  Such  a  slip  of 
paper  may  be  used  as  a  test  for  the  presence  of  actinic  rays. 
By  placing  it  successively  in  the  different  parts  of  the  visi- 
ble spectrum,  it  will  be  affected  least  in  the  red  and  most 
in  the  violet.  The  maximum  actinic  effect  will  be  found 
at  a  point  beyond  the  violet,  wholly  outside  the  visible 
spectrum.  We  thus  detect  ultra-violet  rays  consti- 
tuting an  actinic  spectrum.  Their  position  indicates 
their  high  refrangibility;  that  their  wave-length  is  less 
than  that  of  the  violet  rays.  A  quartz  prism  is  desirable  for 
this  experiment  as  glass  quenches  most  of  the  actinic  rays. 


CHR  OMA  TICS— SPECTRA. 


419 


652.  Curves  of  Intensity.— Fig.  323  represents,  by  means 
of  curves,  the  relative  intensities  of  these  three  properties  of  the 
solar  spectrum  produced  by  a  flint-glass  prism.  The  wave-length 
will  determine  the  position  of  the  ray  in  the  horizontal  band.  The 
greatest  heating  effect  will  be  found  just  beyond  the  red  rays  ;  the 
highest  point  of  the  thermal  curve  is  over  this  part  of  the  spectrum. 
The  greatest  illuminating  effect  will  be  found  a  little  at  the  right  of 
D  (§  638) ;  the  highest  point  of  the  luminous  curve  is  over  this  point. 
The  position  of  greatest  actinic  effect  is  similarly  indicated.  If  a 
rock-salt  or  a  quartz  prism  be  used,  the  curves  will  be  somewhat 


DARK  HEAT  RAYS 


CHEMICAL  RAYS, 


FIG.  323. 

different  from  those  here  shown.  But  it  has  been  found  that  when 
a  spectrum  is  produced,  the  dispersed  rays  are  distributed  very 
unevenly.  Many  more  rays  are  crowded  into  the  red  end  than  into 
the  violet  end.  While,  therefore,  one  part  of  the  spectrum  may 
show  a  greater  heating  effect  than  another  part,  it  does  not  follow 
that  a  single  ray  of  low  refrangibility  has  greater  heating  power 
than  a  single  ray  of  high '  refrangibility.  The  researches  of  Dr. 
Draper,  of  New  York,  go  to  show  that  one  ray  has  a  heating  effect 
equal  to  that  of  any  other  ray  in  the  spectrum.  The  visibility  or 
invisibility  of  certain  rays  depends  on  the  construction  of  the  eye 
rather  than  on  any  peculiarity  of  the  rays  (§649&).  It  is  quite 
possible  that  the  eyes  of  some  animals  are  so  constructed  that  ultra- 
red  rays  may  excite  vision,  and  that  the  eyes  of  other  animals  are  so 
constructed  that  ultra  violet  rays  may  excite  vision. 

653.  The  Electric  Light.— The  electric  light  is  particu- 
larly rich  in. these  invisible  rays.  The  dark  heat  rays  may  be  sifted 
from  the  beam  of  light  by  passing  it  through  a  transparent  solution 
of  alum  ;  only  the  luminous  rays  will  be  allowed  to  pass.  The 
luminous  rays  may  be  sifted  out  by  sending  the  beam  through  an 
opaque  solution  of  iodine  in  carbon  bi-sulphide.  If  these  solutions 


420  CHROMATICS— SPECTRA. 

be  placed  in  spherical  flasks,  they  will  constitute  lenses  which  will 
refract  the  transmitted  rays  to  well  defined  foci.  The  focus  of  the 
transparent  solution  will  be  brilliantly  illuminated,  but  will  have 
little  heating  power  ;  that  of  the  opaque  solution  will  be  invisible, 
while  gun-cotton  placed  there  will  be  instantly  exploded.  Platinum- 
foil  has  been  raised  to  a  red  heat  at  one  of  these  dark  foci. 

654.  Selective  Radiation  and  Absorption. 

— Radiation  of  light  or  heat  consists  in  giving  motion  to 
the  ether ;  absorption  consists  in  taking  motion  from  the 
ether.  Molecules  of  one  kind  are  able  to  vibrate  at  one 
rate ;  those  of  another  kind  may  be  obliged  to  vibrate  at  a 
different  rate.  The  first  set  of  molecules  may  be  able  to 
give  to  the  ether,  or  take  from  it,  a  rate  of  vibration  which, 
in  the  ether,  constitutes  obscure  heat.  These  molecules 
can  absorb  or  radiate  obscure  heat.  They  maybe  unable  to 
vibrate  at  the  higher  rate  which  will  enable  them  to  absorb 
or  radiate  light.  They  must  either  transmit  or  reflect 
light  that  falls  upon  them.  In  other  words,  a  body  ab- 
sorbs with  special  energy  the  kind  of  rays  itself  can  radiate, 
both  the  absorption  and  the  radiation  depending  upon  the 
possible  rate  of  vibration  of  the  molecules  of  the  body. 

(a.)  In  the  case  of  gases,  the  period  of  molecular  vibration  is 
sharply  defined.  Gaseous  molecules,  like  musical  strings,  can 
vibrate  at  only  definite  rates.  Liquid  and  solid  molecules,  like 
sounding-boards,  are  able  to  vibrate  at  different  rates  lying  between 
certain  fixed  limits.  These  limits  depend  largely  upon  the  tem- 
perature. This  principle  underlies  solar,  spectrum  analysis. 

655.  Relation  between  Radiation  and  Ab- 
sorption.— Transparent  bodies  are  transparent  because 
the  ether-waves  which  produce  or  constitute  light  pass  be- 
tween the  molecules  of  such  bodies  without  having  their 
wave-motion  transferred  to  the  molecules.    Diathermanous 
bodies  transmit  heat  freely  because  the  ether-waves  which 
produce  or  constitute  heat  pass  between  the  molecules  of 


CHROMATICS— SPECTRA, 


421 


such  bodies  without  having  their  peculiar  wave-motion 
transferred  to  the  molecules  of  the  body  through  which 
they  pass.  When  a  ray  of  light  or  heat,  in  passing  through 
a  substance,  gives  its  energy  to  the  molecules  between 
which  it  is  passing  in  the  ether,  the  ray  is  absorbed.  It 
no  longer  exists  as  radiant  energy ;  it  has  become  absorbed 
heat,  and  warms  the  body.  It  is  no  longer  a  motion  of  the 
ether ;  it  has  become  a  motion  of  ordinary  matter.  As  in 
the  case  of  radiant  heat,  so  with  light ;  the  best  absorbents 
are  the  best  radiators.  A  piece  of  transparent,  colorless 
glass  will  absorb  very  little  light;  heat  it  intensely,  and 
it  will  radiate  very  little  light.  On 
the  other  hand,  a  piece  of  opaque 
glass  will  absorb  a  great  deal  of 
light ;  when  heated  intensely,  it  will 
radiate  a  great  deal  of  light. 


FIG.  324. 


(a.)  If  an  intensely  heated  pot  of  melted 

lead,  tin  or  plumber's  solder  be  carried 

into  a  dark  place  and  the  dross  skimmed 

aside  by  a  red-hot  iron  ladle,  the  liquid 

metal  (which  in  sunlight 
would  reflect  rather  than 
absorb  the  light)  will  ap- 
pear less  bright  than  the 
surrounding  dross.  If  a 
piece  of  platinum- foil  bear- 
ing'an  ink-mark  be  heat- 
ed to  incandescence  and 
viewed  in  a  dark  room,  the 
ink-mark  will  radiate  more 
light  than  the  metal.  Ex- 
posed to  sunlight,  the  ink- 
mark  will  absorb  more 
light  than  the  metal.  If  a 
chalk-mark  be  made  on  a 
black  poker,  the  poker 
FIG.  325.  heated  red-hot  and  viewed 


422  OPTICAL  INSTRUMENTS. 

in  a  dark  room,  the  chalk  will  be  less  luminous  than  the  iron. 
If  a  piece  of  stone- ware  of  black  and  white  pattern  (Fig.  324)  be 
heated  to  redness  and  viewed  in  a  dark  room,  the  black  will  shine 
more  brightly  than  the  white,  the  pattern  being  reversed  as  shown 
in  Fig.  325. 

EXERCISES. 

1.  Give  the  best  reason  you  can  think  of,  why  the  rainbow  is  a 
circular  arc  and  not  a  straight  line  or  of  some  other  shape. 

2.  Taking  the  velocity  of  light  to  be  188,000  miles  per  second  and 
the  wave-length  for  green  light  to  be  .00002  of  an  inch,  how  many 
waves  per  second  beat  upon  the  retina  of  an  eye  exposed  to  green  light  ? 

3.  How  may  spherical  and  chromatic  aberration  caused  by  a  lens 
be  corrected  ? 

4.  Describe  Fraunhofer's  lines  and  tell  how  they  may  be  produced. 
Why  not  through  a  circular  orifice  ? 

5.  Describe  in  full  what  is  meant  by  dispersion  and  the  dispersive 
power  of  a  medium. 

Recapitulation. — In  this  section  we  have  considered 
the  Dispersion  of  light;  the  Solar  Spectrum 
and  Fraunhofer's  Lines ;  the  Color  of  bodies ; 
the  Rainbow ;  Chromatic  Aberration  and 
Achromatic  Lenses  ;  Luminous,  Thermal 
and  Actinic  Spectra;  the  Electric  Light;  the 
relation  between  Radiation  and  Absorption. 


ECTION   V. 


OPTICAL  INSTRUMENTS.-POLARIZATION. 

656.  Photographers'  Camera. — The  photogra- 
pher's camera  is  nearly  the  same  as  the  camera-obscura 
described  in  §  585.  Instead  of  the  darkened  room  we  have 
a  darkened  box,  BC\  instead  of  the  simple  hole  in  the 
shutter,  we  have  an  achromatic  convex  lens,  placed  in  a 
tube  at  A. 


OP  TIC  A  L  INSTR  UMENTS. 


423 


(a.)  One  part  of  the  box,  B,  slides  within  the  other  part,  C.  A 
ground-glass  plate  is  placed  in  the  frame  at  E,  which  is  adjusted  so 
that  a  well-defined,  inverted  image  of 
the  object  in  front  of  A  is  projected 
upon  the  glass  plate.  This  adjust- 
ment, or  "focussing,"  is  completed 
by  moving  the  lens  and  its  tube  by 
the  toothed  wheel  at  D.  When  the 
"  focussing"  is  satisfactory,  A  is  cov- 
ered with  a  black  cloth,  the  ground-  pIG> 
glass  plate  replaced  by  a  chemically- 
prepared  sensitive  plate,  the  cloth  removed,  and  the  image  pro- 
jected thereon.  The  light  works  certain  chemical  changes  where 
it  falls  upon  this  plate,  and  thus  a  more  lasting  image  is  produced. 
The  preliminary  and  subsequent  processes  necessarily  involved  in 
photography  cannot  be  considered  here;  they  belong  rather  to 
chemistry. 

657.  The  Human  Eye.— This  most  admirable  of 
all  optical  instruments  is  a  nearly  spherical  ball,  capable  of 
being  turned  considerably  in  its  socket.  The  outer  coat,  S, 
is  firm,  and,  excepting  in  front,  is  opaque.  It  is  called  the 
"  white  of  the  eye,"  or  the  sclerotic  coat.  Its  transparent 
part  in  front,  C,  is  called  the  cornea.  The  convexity  of  the 
cornea  is  greater  than  that  of  the  rest  of  the  eyeball. 
Behind  the  cornea  is  an  annular  diaphragm,  /,  called  the 
iris.  It  is  colored  and  opaque  ;  the  circular  window  in  its 

centre  is  called  the  pupil. 
The  color  of  the  iris  consti- 
tutes the  color  of  the  eye. 
Back  of  the  pupil  is  the 
crystalline  lens,  L,  built  of 
concentric  shells  of  varying 
density.  Its  shape  is  shown 
in  the  figure.  This  lens 
divides  the  eye  into  two 
chambers,  the  anterior 


424  OPTICAL  INSTRUMENTS. 

chamber  containing  a  limpid  liquid  called  the  aqueous  hu- 
mor ;  the  posterior  chamber  containing  a  transparent  jelly, 
V,  called  the  vitreous  humor.  The  vitreous  humor  is 
enclosed  in  a  transparent  sack,  H,  called  the  hyaloid  mem- 
brane. The  cornea,  aqueous  humor,  crystalline  lens  and 
vitreous  humor  are  refracting  media.  Back  of  the  hyaloid 
membrane  is  the  retina,  'R,  an  expansion  of  the  optic 
nerve.  Between  the  retina  and  the  sclerotic  coat  is  N, 
the  choroid  coat,  intensely  black  and  opaque.  The  eye, 
optically  considered,  is  simply  an  arrangement  for  pro- 
jecting inverted  real  images  of  visible  objects  upon  a 
screen  made  of  nerve  filaments.  The  image  thus  formed 

is  the  origin  of  the  sensation 
of  vision.  If  this  image  be 
well  defined  and  sufficiently 
luminous  the  vision  is  dis- 
tinct. 

658.  Magnifyiiig- 
Glasses.  —  A  magnifying- 
glass,  or  simple  microscope,  is  a 
convex  lens,  generally  double- 
convex.  The  object  is  placed 
between  the  lens  and  its  prin- 
cipal focus.  The  image  is  vir- 
tual, erect  and  magnified  (Fig- 
312).  The  visual  angle  sub- 
tended by  the  image  is  greater 
than  that  subtended  by  the 
object  (§  587). 

FIG328  659.   Compound  Mi- 

croscope.—The   compound  microscope  consists  of  two 


OPTICAL  INSTRUMENTS. 


425 


or  more  convex  lenses  placed  in  a  tube.  One  of  these,  o, 
called  the  object-glass  or  objective,  is  of  short  focus.  The 
object,  aby  being  placed  slightly  beyond  the  principal  focus, 
a  real  image,  ce?,  •  magnified  and  inverted,  is  formed  within 
the  tube  (§  630).  The  other  lens,  E,  called'  the  eye-glass, 
is  so  placed  that  the  image  formed  by  the  objective  lies 
between  the  eye-glass  and  its  focus.  A  magnified  virtual 
image,  AB,  of  the  real  image  is  formed  by  the  eye-glass 
(§  631)  and  seen  by  the  observer.  (See  Fig.  328.) 

(a.)  Compound  microscopes  are  usually  provided  with  several 
objectives  of  different  focal  distances,  so  that  a  selection  may  be 
made  according  to  the  magnifying  power  required.  The  powers 
generally  used  range  from  50  to  350  diameters  (i.  e.,  they  multiply 
linear  dimensions  so  many  timesX  The  object  generally  needs  to 
be  intensely  illuminated  by  a  concave  mirror  or  convex  lens. 


FIG.  329. 

66O.  Galilean  Telescope;  Opera  Glass.— In 

the  telescope  attributed  to  Galileo  the  objective  is  a  double 
convex,  and  the  eye-piece  a  double  concave  lens.  The 
concave  lens  intercepts  the  rays  before  they  have  reached 
the  focus  of  the  objective ;  were  it  not  for  this  eye-piece,  a 
real,  inverted  image  would  be  formed  back  of  the  position 
of  the  concave  lens.  The  rays  from  A,  converging  after 
refraction  by  0,  are  rendered  diverging  by  (7;  they  seem  to 
diverge  from  a.  In  like  manner,  the  image  of  B  is  formed 
at  b.  The  image  ab  is  erect  and  very  near.  An  opera- 
glass  consists  of  two  Galilean  telescopes  placed  side  by 
side.  In  a  good  instrument  both  lenses  are  achromatic. 


426 


OPTICAL  INSTRUMENTS. 


661.  Astronomical  Telescope;  Refractor. — 

Astronomical  telescopes  are  of  two  kinds — refractors  and 
reflectors.  "Fig.  330  represents  the  arrangement  of  the 
lenses  and  the  direction  of  the  rays  in  the  refracting 
telescope.  The  object-glass  is  of  large  diameter  that  it 


FIG.  330. 

may  collect  many  rays  for  the  better  illumination  of  the 
image.  The  inverted,  real  image  formed  by  the  objective, 
0,  is  magnified  by  the  eye-piece,  as  in  the  case  of  the 
compound  microscope.  The  visible  image,  cd,  is  a  virtual 
image  of  ab,  the  real  image  of  AB. 

662.  Reflecting  Telescopes.— A  reflecting  tele- 
scope consists  of  a  tube  closed  at  one  end  by  a  concave 


FIG.  331. 


mirror,  so  placed  that  the  image  thus  formed  may  be  mag- 
nified by  a  convex  lens  used  as  an  eye-piece.  Sometimes 
the  eye-piece  consists  of  a  series  of  convex  lenses  placed 
in  a  horizontal  tube,  as  shown  in  Fig.  331.  The  rays 
from  the  mirror  are  reflected  by  the  cathetal  prism  mn 
(§  621  [<?]),  and  a  real  image  formed  at  ab.  This  image  is 


OPTICAL  INSTRUMENTS. 


427 


magnified  by  the  glasses  of  the  eye-piece  and  a  virtual 
image  formed  at  cd.  The  Earl  of  Rosse  built  a  telescope 
with  a  mirror  six  feet  in  diameter  and  having  a  focal  dis- 
tance of  fifty-four  feet. 

663.  Terrestrial  Telescope. — The  inversion  of 
the  image  in  an  astronomical  telescope  is  inconvenient 


FIG.  332. 

when  viewing  terrestrial  objects.  This  inconvenience  is 
obviated  in  the  terrestrial  telescope  by  the  interposition  of 
two  double  convex  lenses,  m,  n,  between  the  objective  and 
the  eye-piece.  The  rays,  diverging  from  the  inverted 
imago  at  /,  cross  between  m  and  n,  and  form  an  erect, 
magnified,  virtual  image  at  db. 


FIG.  333- 

664.  Magic  Lantern. — In  the  magic  lantern,  a 
lamp  is  placed  at  the  common  focus  of  a  convex  lens  in 
front  of  it  and  of  a  concave  mirror  behind  it.  The  light 
is  thus  concentrated  upon  db,  a  transparent  picture,  called 
the  "slide."  A  system  of  lenses,  m,  is  placed  at  a  little 


428 


OPTICAL  INSTRUMENTS. 


more  than  its  focal  distance  (§  630)  beyond  the  slide.  A 
real,  inverted,  magnified  image  of  the  picture  is  thus  pro- 
jected upon  the  screen  8.  The  tube  carrying  m  is  adjust- 
able, so  that  the  foci  may  be  made  to  fall  upon  the  screen 
and  thus  render  the  image  distinct.  By  inverting  the 
slide  the  image  is  seen  right  side  up.  The  solar  and 

electric  microscopes 
act  in  nearly  the  same 
way,  the  chief  differ- 
ence being  in  the 
source  of  light. 


(a.)  Directions  for 
making  a  simple  magic 
lantern  may  be  found  on 
page  84  of  Mayer  and 
Barnard's  little  book  on 
FIG.  334.  Light.  Fig.  334  repre- 

sents a  very  compact  and 

efficient  lantern,  known  as  Marcy's  Sciopticon,  and  furnished  by 
Ritchie,  of  Boston.     (See  Dolbear's  Art  of  Projecting.) 

665.  Stereoscopic  Pictures.— Close  the  left  eye 
and  hold  the  right  hand  so  that  the  forefinger  shall  hide 
the  other  three  fingers.  Without  changing  the  position 
of  the  hand,  open  the  left  and  close  the  right  eye.  The 
hidden  fingers  become  visible  in 
part.  Place  a  die  on  the  table 
directly  in  front  of  you.  Look- 
ing at  it  with  only  the  left  eye, 
three  faces  are  visible,  as  shown 


FIG.  335. 


at  A,  Fig.  335.  Looking  at  it  with  only  the  right  eye,  it 
appears  as  shown  at  B.  From  this  we  see  that  when  we 
look  at  a  solid,  the  images  upon  the  retinas  of  the 
two  eyes  are  different.  If  in  any  way  we  combine  two 


POLARIZATION.  429 

drawings,  so  as  to  produce  images  upon  the  retinas  of  the 
two  eyes  like  those  produced  by  the 
solid  object,  we  obtain    the  idea  of 
solidity. 

666.  The    Stereoscope.— To 

blend  these  two  pictures  is  the  office 
of  the  stereoscope.  Its  action  will 
be  readily  understood  from  Fig.  336. 
The  diaphragm  D  prevents  either  eye 
from  seeing  both  pictures  at  the  same 
time.  Kays  of  light  from  B  are  re- 
fracted by  the  half-lens  E'  so  that  they 

seem  to  come  from  C.     In  the  same 

FIG.  336. 
way,  rays  from  A  are  refracted  by  E  so 

that  they  also  seem  to  come  from  C.  The  two  slightly 
different  pictures  thus  seeming  to  be  in  the  same 
place  at  the  same  time  are  successfully  blended,  and 
the  picture  "stands  out,"  or  has  the  appearance  of 
solidity.  If  the  two  pictures  of  a  stereoscopic  view  were 
exactly  alike,  this  impression  of  solidity  would  not  be  pro- 
duced. 

667.  Polarization. — If  a  horizontal  string,  tightly 
drawn,  be  hit  a  vertical  blow,  a  wave  will  be  formed  with 
vibrations  in  a  vertical  plane.     If  the  string  be  hit  a 
horizontal  blow,  a  wave  will  be  formed  with  vibrations  in 
a  horizontal  plane.    Thus  a  transversal  wave  is  capable  of 
assuming  a  particular  side  or  direction  while  a  longitudinal 
wave  is  not.    This  is  expressed  by  saying  that  a  transversal 
wave  is  capable  of  polarization.     Polarization  of  light 
may  be  produced  in  three  ways — by  absorption,  by  reflec- 
tion and  by  double  refraction. 


430 


POLARIZATION. 


FIG.  337. 


FTG.  338. 


668.  Planes  of  Vibration  in  Sunbeam.— If 

we  imagine  a  sunbeam  to  be  cut  by  a  plane 
perpendicular  to  the  direction  of  the  beam, 
we  may  suppose  the  section  to  consist  of 
vibrations  moving  in  every  possible  plane,  as 
represented  by  Fig.  337.  It  is  not  to  be 
supposed  that  all  of  these  planes  will  inter- 
sect at  the  same  point.  There  will  be  many  rays  whose 
planes  of  vibration  are  vertical,  many  whose  planes  of 
vibration  are  horizontal,  etc. 

669.  Polarization  by  Absorp- 
tion.— If  a  sunbeam  fall  upon  a  substance 
whose  molecular  structure  allows  vibrations 
in  only  a  particular  plane,  say  vertical,  the 
substance  may  be  compared  to  a  frame  with 
vertical  bars,  as  represented  by  Fig.  338. 

Such  a  frame  or  such  a  substance  will  absorb  the  rays 
whose  vibrations  lie  in  a  plane  that  is  horizontal  or  nearly 
so,  convert  them  into  absorbed  heat,  and  transmit,  as 
polarized  light,  those  rays  whose  vibrations  lie  in  a  plane 
that  is  vertical  or  nearly  so.  A  plate  cut 
in  a  certain  way  from  a  crystal  of  tour- 
maline acts  in  such  a  way;  it  is  called  a 
tourmaline  analyzer.  If  the  sunbeam  fall 
upon  a  substance  that  allows  vibrations 
in  only  a  horizontal  plane,  the  substance 
may  be  compared  to  a  frame  with  hori- 
zontal bars,  as  represented  in  Fig.  339.  Such  a  body  will 
quench  all  the  rays  whose  vibrations  lie  in  a  plane  that  is 
vertical  or  nearly  so,  and  transmit,  as  polarized  light,  those 
rays  whose  vibrations  lie  in  a  plane  that  is  horizontal  or 


FIG.  339. 


POLARIZA  TION. 


431 


nearly  so.    The  tourmaline  analyzer  previously  used  acts 
in  this  way  when  turned  a  quarter  way  around. 

67O,  Tourmaline  Tongs. — If  these  two  frames,  or 
two  tourmaline  analyzers,  be  placed  one  over  the  other  in 
such  a  way  that  the  bars  of  the  second  shall  be  perpen- 
dicular to  those  of  the 
first,  it  will  be  seen  that 
the  first  will  quench  or 
absorb  part  of  the  rays,  FlG 

while  the  rays  trans- 
mitted by  the  first  as  polarized  light  will  be  quenched  by 
the  second.  But  if  the  bars  of  the  second  be  parallel  to 
those  of  the  first,  the  polarized  light  transmitted  by  the 
first  will  also  be  transmitted  by  the  second.  This  partial 
or  total  absorption  of  luminous  rays  is  shown  easily  with 
the  "  tourmaline  tongs,"  which  consist  of  two  tourmaline 
plates  set  in  movable  discs  (Fig.  340).  Light  transmitted 
by  either  plate  is  polarized  (and  colored  by  the  accidental 
tint  of  the  tourmaline).  When  the 
plates  are  superposed,  polarized 
light  may  be  transmitted  by  both, 
or  all  of  the  incident  light  may  be 
absorbed  according  to  their  relative 
positions  as  above  stated. 


FIG.  341. 


671.  Polarization  by  Re- 
flection. —  Light  is  polarized 
when  the  rays  whose  vibrations  lie  in  a  particular  plane  are 
alone  allowed  to  pass.  This  effect  may  be  produced  by 
causing  a  beam  of  light  to  be  reflected  by  a  non-metallic 
mirror  at  a  certain  angle  which  depends  upon  the  nature 
of  the  reflecting  substance.  For  glass,  the  ray  must  make 


432 


POLARIZATION. 


D 


with  the  reflecting  surface  an  angle  of  35°  25'  (angle  of 
incidence  =  54°  35'). 

612.  Malus's  Polariscope.— This  instrument  has 

two  reflectors  made  of 
bundles  of  glass  plates. 
Of  these,  A  is  called 
the  polarizer  and  B  the 
analyzer.  Both  reflect- 
ors turn  upon  horizon- 
tal axes ;  B  also  turns 
upon  a  vertical  axis  by 
means  of  the  horizontal 
circles  CO.  When  A 
and  B  are  placed  at  the 
polarizing  angle  with 
the  vertical  axis,  a  beam 
of  light  is  made  to  fall  upon  the  polarizer  in  such  a  direc- 
tion that  the  reflected  light  will  pass  vertically  upward  to 
B.  This  reflected  light  will  be  polarized.  The  polarized 
light  will  be  reflected  by  B  when  the  second  reflector  is 
parallel  to  the  first  (Fig.  343) ;  it  will  be  absorbed  or 
transmitted  when  B  is  perpendicular  to  A  (Fig.  342). 

(a.)  Place  B  as  shown  in  Fig.  343.  Throw  a  beam  of  light  upon 
A,  the  room  being  darkened.  The  light  reflected  from  S  will  form 
a  white  spot  upon  the  side  of  the  room.  Turn  the  collar  C  slowly 
around.  The  spot  of  light  will  move  around  the  sides  of  the 
room  gradually  growing  fainter.  When  C  has  been  turned  a 
quarter  way  around  (Fig.  342)  the  spot  has  wholly  disappeared. 
Beyond  this  it  grows  brighter  until  C  has  been  turned  half  way 
around,  when  it  is  as  bright  as  at  the  b«ginning.  When  C  has 
been  turned  three-quarters  around,  the  spot  again  disappears, 
again  reappearing  as  C  and  B  are  brought  to  their  original 
positions. 


FIG.  342. 


FIG.  343. 


OPTICAL  INSTRUMENTS.  433 

673.  Dotible  Refraction. — We  have  seen  that  a 
plate  of  tourmaline  may  stop  all  rays  whose  vibrations  lie 
in  a  certain  plane  while  it  allows  passage  to  all  rays  whose 
vibrations  lie  in  a  plane  perpendicular  to  this.  A  crystal 
of  Iceland  spar  shows 
a  different  but  very 
important  effect  upon 
an  incident  beam. 
The  retardation  of 
those  vibrations  whose 
plane  is  parallej  to  the 
axis  (the  line  joining  FIG.  344. 

the  two  obtuse  angles 

of  the  crystal)  is  different  from  the  retardation  of  those 
vibrations  whose  plane  is  perpendicular  to  the  axis.  This 
difference  in  change  of  velocity  produces  a  difference  in  the 
refraction  of  the  two  sets  of  rays.  A  beam  of  light,  there- 
fore, falling  upon  a  crystal  of  Iceland  spar  will  be  gener- 
ally split  into  two,  producing  the  effect  known  as  double 
refraction. 


(a.)  A  small  object,  as  a  dot  or  line,  viewed  through  a  crystal  of 
Iceland  spar,  will  generally  show  two  images  formed  by  light  oppo- 
sitely polarized.  If  the  eye  be  placed  directly  above  the  dot  and 
the  crystal  slowly  turned  around,  one  image  known  as  the  ordinary 
image  will  remain  stationary,  while  the  other  known  as  the  extra- 
ordinary image  will  revolve  about  it  at  a  varying  distance.  The 
ordinary  ray  has  a  constant  and  the  extraordinary  ray  a  variable 
index  of  refraction. 

(&.)  On  looking  at  the  two  images  formed  by  double  refraction 
through  a  tourmaline  or  any  other  analyzer,  it  will  be  found  that 
there  is  a  marked  difference  in  the  brightness  of  the  two  images. 
As  the  analyzer  is  turned  around,  one  image  grows  brighter  and  the 
other  fainter,  the  greatest  brightness  of  one  being  simultaneous 
with  the  extinction  of  the  other. 
19 


434  ENERGY. 

Recapitulation. — In  this  section  we  have  considered 
the  Photographer's  Camera  and  the  human 
Eye ;  Microscopes  and  Telescopes ;  the  Magic 
Lantern  and  the  Stereoscope  ;  Polarization 
of  light  by  Absorption,  by  Reflection  and  by 
Double  Refraction. 


CONCLUSION. 

ENERGY.  • 

674.  Varieties  of  Energy. — Like  matter,  energy 
is  indestructible.    "We  have  already  seen  that  energy  may 
be  visible  or  invisible   (i.  e.,  mechanical  or  molecular), 
kinetic  or  potential.     We  have  at  our  control  at  least 
eight  varieties  of  energy. 

(a.)  Mechanical  energy  of  position  (visible,  potential). 
(&.)  Mechanical  energy  of  motion  (visible,  kinetic). 
(c.)  Latent  heat  (molecular,  potential). 
(d.)  Sensible  heat  (molecular,  kinetic). 
'(e.)  Chemical  separation  (molecular  or  atomic  ;  potential). 
(/.)  Electric  separation  (probably  molecular,  potential). 
(g.)  Electricity  in  motion  (probably  molecular,  kinetic). 
(h.)  Radiant  energy,   thermal,   luminous  or  actinic  (molecular, 
kinetic). 

675.  Conservation  of  Energy. — The  doctrine 
that,  considering  the  universe  as  a  whole,  the  sum  of  all 
these  forces  is  a  constant  quantity,  is  known  as  the  Con- 
servation, of  Energy. 

a  +  b  +  c  +  d  +  e+f+g  +  fi  =  a.  constant  quantity. 

This  does  not  mean  that  the  value  of  a  is  invariable ;  we 
have  seen  it  changed  to  other  varieties  as  b  or  d.    We  have 


ENERGY.  435 

seen  heat  changed  to  electricity  and  vice  versa,  and  either 
or  both  changed  to  mechanical  energy.  It  does  not  mean 
that  the  sum  of  these  eight  variable  quantities  in  the  earth 
is  Constant,  for  we  have  seen  that  energy  may  pass  from 
sun  to  earth,  from  star  to  star.  But  it  does  mean  that  the 
sum  of  all  these  energies  in -all  the  worlds  that  constitute 
the  universe  is  a  quantity  fixed,  invariable. 

676.  Correlation  of  Energy.— The  expression 
Correlation  of  Energy  refers  to  the  convertibility  of  one 
form  of  energy  into  another.     Our  ideas  ought,  by  this 
time,  to  be  clear  in  regard  to  this  convertibility.    One  im- 
portant feature  remains  to  be  noticed.    Kadiant  energy  can 
be  converted  into  other  forms,  or  other  forms  into  radiant 
energy  only  through  the  intermediate  state  of  absorbed 
heat. 

677.  A  Prose  Poem. — "A  river,  in  descending  from  an 
elevation  of  7720  feet,  generates  an  amount  of  heat  competent  to 
augment  its  own  temperature  10°  F.,  and  this  amount  of  heat  was 
abstracted  from  the  sun,  in  order  to  lift  the  matter  of  the  river  to 
the  elevation  from  which  it  falls.     As  long  as  the  river  continues 
on  the  heights,  whether  in  the  solid  form  as  a  glacier,  or  in  the 
liquid  form  as  a  lake,  the  heat  expended  by  the  sun  in  lifting  it 
has  disappeared  from  the  universe.    It  has  been  consumed  in  the 
act  of  lifting.     But,  at  the  moment  that  the  river  starts  upon  its 
downward  course,  and  encounters  the  resistance  of  its  bed,  the  heat 
expended  in  its  elevation  begins  to  be  restored.     The  mental  eye, 
indeed,  can  follow  the  emission  from  its  source  through  the  ether, 
as  vibratory  motion,  to  the  ocean,  where  it  ceases  to  be  vibration, 
and  takes  the  potential  form  among  the  molecules  of  aqueous  vapor  ; 
to  the  mountain-top,  where  the  heat  absorbed  in  vaporization  is  given 
out  in  condensation,  while  that  expended  by  the  sun  in  lifting  the 
water  to  its  present  elevation  is  still  unrestored.     This  we  find  paid 
back  to  the  last  unit  by  the  friction  along  the  river's  bed ;  at  the 
bottom  of  the  cascade,  where  the  plunge  of  the  torrent  is  suddenly 
arrested  ;  in  the  warmth  of  the  machinery  turned  by  the  river  ;  in 
the  spark  from  the  millstone  ;  beneath  the  crusher  of  the  miner :  in 


436 


REVIEW. 


the  Alpine  saw-mill ;  in  the  milk-churn  of  the  chalet ;  in  the  sup- 
ports of  the  cradle  in  which  the  mountaineer,  by  water-power,  rocks 
his  baby  to  sleep.  All  the  forms  of  mechanical  motion  here  indi- 
cated are  simply  the  parcelling  out  of  an  amount  of  calorific  motion 
derived  originally  from  the  sun  ;  and,  at  each  point  at  which  the 
mechanical  motion  is  destroyed  or  diminished,  it  is  the  sun's  heat 
which  is  restored." — TyndalL 


678.  Recapitulation. 

f  VISIBLE    OR    MECHANICAL. 
HEAT 


INVISIBLE   OR 
MOLECULAR. 


LIGHT 


ELECTRICITY...  J 


OF  POSITION,  e.  g.,  Hanging  Ap- 
Potential.          pie,     Hedd    of 
Water. 

OF  MOTION,  e.  g.,  Falling  Apple, 
Kinetic.  Flowing  Water. 

OF  POSITION,  e.  g.,  Latent  Heat. 
Potential. 

OF  MOTION,  e.  g.,  Sensible  Heat. 
Kinetic. 

OF  MOTION,  or 
Kinetic. 

OF  POSITION,  e.  g.,  Charged  Ley- 
Potential.  den  jar,  Battery 

ivith  circuit  bro- 
k<n. 

OF  MOTION,  e.  g.,  Leydenjar  dis- 
Kinetic.  charging :   Bat- 

tery   with    cir- 
cuit closed. 


GENEEAL  KEVIEW. 

1.  (a.)  Define  science,  matter,  mass,  molecule  and  atom.     (&.)  How 
do  physical  and  chemical  changes  differ  ?    (c.)  Define  physics. 

2.  (a.)  What  are  chemical  and  physical  properties  of  matter? 
(ft.)    Define  and  illustrate  two  universal  and    one    characteristic 
properties  of  matter. 

3.  (a.)  Define  meter,  liter  and  gram.     •(&.)  What  is  a  solid,  a 
liquid,  and  a  gas  ?    (c.)  Define  dynamics  and  force. 

4.  (a.)  Name  and  define  three  units  of  force.     (&.)  Give  Newton's 
Laws  of  Motion,     (c.)  Give  the  law  of  reflected  motion. 


REVIEW.  437 

5.  (a.)  Explain  the  parallelogram  of  forces,  and  (6.)  the  polygon 
of  forces. 

6.  (a.)  Define  gravitation  and  give  its  laws.    (6.)  Give  the  law  of 
weight,     (c.)  What  is  the  centre  of  gravity,  and  how  may  it  be 
found  ? 

7.  (a.)  Describe   Att wood's  machine.      (5.)    Give  the  rules  and 
formulas  for  falling  bodies,    (c.)  How  far  will  a  body  fall  in  three 
seconds  ? 

8.  (a.)  What  is  a  pendulum  ?    (&.)  Give  the  laws  of  the  pendulum, 
(e.)  How  long  must  a  pendulum  be  to  vibrate  10  times  a  minute  ? 

9.  (a.)  Define  energy,   foot-pound,  dyne,  erg,  and  horse-power. 
(6.)  Deduce  the  formula  for  measuring  kinetic  energy  when  weight 
and  velocity  are  given. 

10.  («.)  Define  each  of  the  six  traditional  simple  machines.     (6.) 
Give  the  law  for  each,    (c.)  What  is  the  office  of  a  machine  ?    (d.\ 
Discuss  the  subject  of  friction. 

11.  («.)  Give  Pascal's  law,  and  the  rule  for  determining  lateral 
liquid  pressure.    (6.)  Describe  the  hydrostatic  press,  and  state  the 
general  principle  upon  which  its  action  depends. 

12.  (a.}  State  Archimedes'  principle.    (6.)  What  is  specific  gravity  ? 
(c.)  Explain  the  determination  of  the  sp.  gr.  of  a  solid  lighter  than 
water,    (d.)  Explain  the  use  of  the  specific  gravity  bulb,      (e.) 
Describe  Nicholson's  hydrometer  and  explain  its  use. 

13.  (a.)  A  1000  gr.  bottle  having  in  it  928  grs.  of  water,  has  the 
remaining  space  filled  with  metallic  sand  and  then  weighs  1126.75. 
What  is  the  sp.  gr.  of  the  sand  ?    (5.)  Through  which  of  the  three 
kinds  of  levers  can  the  greatest  power  be  gained  ?    (c.)  Through 
which  can  none  be  gained  ?    (d.)  Why  do  we  use  it  ?    (e.)  Give  an 
example. 

14.  A  ball  projected  vertically  upward,  returns  in  15  seconds  to 
the  place  of  projection.     How  far  did  it  ascend  ? 

15.  (a.)  A  floating  solid  displaces  how  much  liquid  ?    (6.)  An 
immersed  solid  displaces  how  much  liquid  ?    (c.)  A  floating  solid 
loses  how  much  weight  ?    (d.)  An  immersed  solid  loses  how  much 
weight  ? 

16.  What  is  the  energy  of  a  rifle-ball  weighing  32  grams,  having 
a  velocity  of  213  meters  per  second,  and  striking  in  the  centre  of  a 
pendulum  of  wood  weighing  23  kilograms? 

17.  (fi.)  What  is  meant  by  the  increment  of  velocity  or  gravity  ? 
(6.)  How  far  will  a  body  fall  in  6|  seconds?    (e.)  How  far  in  the 
9th  second?    (a.)  If  a  freely-falling  body  have  a  velocity  of  448  ft. 
per  second,  how  long  has  it  been  falling  ? 

18.  (a.)  Deduce,  from  the  laws  of  falling  bodies,  the  formula  for 


438  REVIEW. 

the  velocity  of  spouting  liquids  (u  =  8.02  <x/A).  (&.)  Why  must  the 
unit  of  measure  used  with  this  formula  be  feet  ?  (c.)  Deduce  a 
similar  formula  in  which  the  meter  is  involved  as  the  unit. 

19.  Name  four  kinds  of  water-wheels,  and  describe  the  most 
efficient  of  them. 

20.  (a.)  Explain  the  action  of  the  mercury  barometer,    (b.)  Give 
Mariotte's  law.    (c.)   Describe  the  piston  of  Sprengel's  air-pump. 
(d.)  Describe  the  ordinary  air-pump,     (e.)  Explain  the  action  of  the 
siphon. 

21.  (a.)  How  would  you  illustrate  the  law  of  magnetic  attraction 
and  repulsion  ?    (&.)  Give  the  theory  of  magnetic  fluids,     (c.)  What 
do  you  think  of  its  accuracy  and  value?    (d.)  Explain  magnetic 
induction. 

22.  If  the  capacity  of  the  barrel  of  an  air-pump  be  }  that  of  the 
receiver,  how  much  air  would  remain  in  the  receiver  at  the  end  of 
the  fourth  stroke  of  the  piston,  and  what  would  be  its  tension 
compared  with  that  of  the  external  air  ? 

23.  What  is  the  pressure  on  the  side  of  a  reservoir  150  feet  long, 
and  filled  with  water  to  the  height  of  twenty  feet  ? 

24.  (a.)  Why  is  a  reservoir  usually  built  in  connection  with 
water- works  ?     (6.)   Why  are  fire-engines  provided  with  an  air- 
chamber?      (c.)    Why  should    the    nozzle    be    smaller   than    the 
hose? 

25.  (ff.)  Why  can  you  not  raise  water  50  feet  with  a  common 
pump  ?    (6.)  What  change  would  it  be  necessary  to  make  in  the 
pump  in  order  to  raise  water  to  that  height  ?    (c.)  Illustrate  by  a 
diagram. 

26.  (a.)  Give  the  law  of  electrical  attraction  and  repulsion,  and 
illustrate  by  pith-ball  electroscope.     (6.)  Define  conductors  and  non- 
conductors, electrics  and  non-electrics,     (c.)  Illustrate  by  an  example 
of  each. 

27.  (a.)  Give  and  illustrate  each  of  the  laws  of  motion.    (6.) 
Explain  composition  and  resolution  of    forces   with   illustrative 
figures. 

28.  (a.)  Give  the  facts  of  gravity  and  the  law  of  weight.     (&.) 
If  a  body  weigh  120  Ibs.  2500  miles  below  the  surface  of  the  earth, 
at  what  distance  above  the  surface  will  it  weigh  80  Ibs.  ? 

29.  Explain  and  illustrate  electric  induction  fully. 

30.  (a.)  Explain  the  construction  and  action  of  the  electrophorus. 
What  kind  of  electricity  is  discharged  from  it  ?    (6.)  Describe  the 
Leyden  jar  and  explain  its  action,     (c.)  Explain  the  action  of  the 
plate  electric  machine,     (d.)  lu  what  way  do  lightning-rods  protect 
buildings  ? 


REVIEW.  439 

31.  (a.)  Discuss  carefully  the  resistance  of  a  Galvanic  cell.    (6.) 
Describe  the  Voltaic  arc. 

32.  (a.)  State  the  difference  between  a  magnet  and  an  electro- 
magnet.   (&.)  Give  the  principles  on  which  the  telegraph  operates. 
(c.)  What  is  meant  by  an  "electronegative  substance?" 

33.  (a.)  Describe  Ruhinkorff's  coil,  and  (6.)  explain  its  action. 

34.  Describe  the  thermo-electric  pile,  and  explain  its  use. 

35.  (a.}  Give  Prof.  Tyndall's  illustration  of  the  propagation  of 
sound.    (6.)  What  is  the  velocity  of  sound  in  air  ?    (c.)  How  is  it 
affected  by  temperature  ? 

36.  (a.)  Explain  the  difference  between  noise  and  music.     (&.) 
Name  the  three  elements  of  a  musical  sound,  and  state  the  physical 
cause  of  each. 

37.  (a.)  Describe  and  explain  the  telephone.     (6.)  The  phono- 
graph. 

38.  (a.)   Explain  interference  of  sound.     (6.)   Give  the  laws  of 
vibration  of  musical  strings,     (c.)   Give  the  relative  numbers  of 
vibration  for  the  tones  of  the  major  diatonic  scale. 

39.  (a.)  If  18  seconds  intervene  between  the  flash  and  report  of  a 
gun,  what  is  its  distance,  temperature  being  82°  F.  ?     (6.)    If  a 
musical  sound  be  due  to  144  vibrations  per  second,  how  many 
vibrations  correspond  to  its  3d,  5th,  and  octave  ? 

40.  The  bottom  of  a  tank  is  100  centimeters  on  one  side,  and  a 
meter  on  the  adjoining  side.    The  tank  has  a  depth  of  50  centi- 
meters of  water,    (a.)  What  is  the  pressure  on  the  bottom  ?    (6.) 
On  either  one  of  the  vertical  sides  ? 

41.  («.)  What  is  a  horse-power?    (&.)  How  many  horse-powers 
are  there  in  a  machine  that  will  raise  8250  Ibs.  176  ft.  in  4  minutes  ? 
(c.)  State  the  modes  of  diminishing  friction. 

42.  What  will  be  the  kinetic  energy  of  a  25-pound  ball  that  has 
fallen  a  mile  ?    (Reject  small  remainders.) 

43.  Two  bodies  are  attracting  a  third  with  forces  as  441  to  576, 
the  first,  weighing  25  Ibs.,  at  a  distance  from  the  third  of  20  feet, 
and  the  second  at  a  distance  of  30  feet ;  what  is  the  weight  of  the 
second  ? 

44.  How  far  will  a  body  fall  in  the  first  second  on  Saturn,  the 
density  of  Saturn  being  .12  that  of  the  earth,  and  its  diameter  being 
72000  miles  ? 

45.  (a.)  What  is  temperature  ?     (&.)   Discuss  the  expansion  of 
water  by  heat,     (c.)  What  is  the  rate  of  gaseous  expansion  by  heat  ? 

46.  (a.)  What  is  the  difference  between  evaporation  and  boiling  ? 
(&.)  What  is  the  boiling  point  ?    (c.)  What  is  distillation,  and  how 
is  it  performed  ? 


440  REVIEW. 

47.  (a.)  Define  latent,  sensible  and  specific  heat.    (&.)  What  is  the 
latent  heat  of  water  and  of  steam  ? 

48.  (a.)  Explain  the  several  modes  of  diffusing  heat,  showing 
how  they  differ.    (&.)  State  and  explain  the  relation  between  the 
absorbing  and  radiating  powers  of  any  given  substance. 

49.  (a.)   What  is  thermodynamics?    (&.)  State  the  first  law  of 
thermodynamics,     (c.)  What  is  the  mechanical  equivalent  of  heat 
in  kilograrnmeters  ?    (d.)  What  does  your  answer  mean  ? 

50.  (a.)  Draw  a  figure  showing  the  position  of  the  parts  of  the 
cylinder  and  steam-chest  when  the  piston  is  going  up. 

51.  (a.)    To  what  temperature  would  a  cannon-ball  weighing 
150  Ibs.  and  moving  1920  feet  a  second,  raise  2000  Ibs.  of  water 
from  32°  F.,  if  its  motion  were  suddenly  converted  into  heat  ?    (6.) 
Explain  the  origin  and  propagation  of  sound  waves. 

52.  (a.)  Express  a  temperature  of  50°  F.  in  degrees  centigrade. 
(6.)  Name  and  describe  the  essential  parts  of  a  steam-engine  in  their 
proper  order,    (c.)  Point  out  the  changes  in  form  of  energy  from 
the  furnace  fire,  through  a  high-pressure  engine  to  the  heated  axles 
set  in  motion  thereby. 

53.  The  mechanical  equivalent  of  heat  being  1390  foot-grams, 
the  foot  being  equal  to  30.48cm.,  and  the  increment  of  velocity  on 
the  earth  being  980cm.,  find  the  mechanical  equivalent  in  ergs. 

Ans.  41519856. 

54.  (a.)  What  is  the  difference  between  waves  of  sound  and 
waves  of  light  ?    (6.)  What  is  the  difference  between  an  atherma- 
nous  and  an  opaque  substance  ?    (c.)  What  determines  the  apparent 
size  of  a  visible  object  ? 

55.  (a.)  If  the  gun-cotton  mentioned  in  §  555  (a.)  be  rubbed  with 
a  little  lamp-black,  will  it  be  ignited  with  more  or  less  difficulty  ? 
Why?    (&.)  What  is  reflection  of  light?    (c.)  How  does  it  differ 
from  refraction  of  light  ? 

56.  (a.)  How  could  you  show  that  light  is  invisible  unless  it  en- 
ters the  eye?    (&.)  What  determines  the  apparent  position  of  an 
object?     (c.)  What  is  the  distinction  between  real  and  virtual 
images  ? 

57.  (a.)  Describe  and  illustrate  a  construction  for  conjugate  foci 
in  the  case  of  a  concave  mirror.     (6.)  In  the  case  of  a  convex  lens, 
(c.)  What  is  meant  by  the  index  of  refraction  ?    (d.)  Give  the  laws 
for  refraction  of  light. 

58.  (a.)  Explain  total  internal  reflection.    (&.)  What  is  meant  by 
dispersion  of  light?    (c.)  What  is  pure  spectrum  and  how  may  it 
be  produced  ?    (<?.)  What  are  Fraunhofer's  Lines  and  what  do  they 
indicate?    (e.)  Name  the  prismatic  colors  in  order. 


REVIEW.  441 

59.  (a.)  Why  does  a  certain  piece  of  glass  look  red  when  it  is 
held  between  a  lamp  and  the  eye  ?    (6.)  Why  does  it  look  red  when 
the  lamp  is  between  the  glass  and  the  eye  ?    (c.)  Explain  the  suc- 
cession of  colors  in  the  rainbow,     (d.)  What  three  classes  of  rays  in 
a  sunbeam  ? 

60.  (a.)  Describe  the  human  eye  as  an  optical  instrument.   (6.)  The 
opera-glass,     (c.)  The  terrestrial  telescope.    (rf.)  The  stereoscope. 

61.  (a.)   Explain   polarization  of  light  by  absorption.     (6.)   By 
reflection. 

62.  (a.)  Explain  the  action  of  the  siphon.     (6.)  Find  the  volume 
of  a  balloon  filled  with  hydrogen  that  has  a  lifting  power  of  440  Ibs. 
(sp.  gr.  of  air  —  14.42.     One  liter  of  hydrogen  weighs  .0896^.) 

63.  (a.)  The  barrel  of  an  air-pump  is  £  that  of  the  receiver ;  find 
the  tension  of  the  air  in  the  receiver  after  8  strokes  of  the  piston,  call- 
ing the  normal  pressure  15  Ibs.  and  disregarding  the  volume  of  the 
connecting  pipes.     (&.)  A  stone  let  fall  from  the  top  of  a  cliff  was 
seen  to  strike  the  bottom  in  6^  seconds  ;  how  high  was  the  cliff  ? 

64.  (a.)  A  ship  passing  from  the  sea  into  a  river,  discharges  44800 
Ibs.  of  cargo,  and  is  found  to  sink  in  the  river  to  the  same  mark  as 
in  the  sea.  The  sp.  gr.  of  sea-water  being  1.028,  find  the  weight  of  the 
ship  and  cargo.    (6.)  A  body  weighing  12  Ibs.  (sp.  gr.  =  |,)  is  fastened 
to  the  bottom  of  a  vessel  by  a  cord.     Water  being  poured  in  until 
the  body  is  covered,  find  the  tension  of  the  cord. 

65.  (a.)  If  the  intensity  of  gravity  at  the  moon  be  ^  of  that  at  the 
earth,  find  the  length  of  a  seconds  pendulum  at  the  moon,  the  length 
of  one  at  the  earth  being  39.1  inches.    (6.)  Find  the  maximum  weight 
that  can  be  supported  by  a  hydraulic  elevator  connected  with  a 
reservoir,  the  area  of  the  piston  being  24  sq.  in.  and  the  reservoir 
being  170  ft.  above  the  cylinder,     (c.)  The  difference  between  the 
fundamental  tones  of  two  organ-pipes  of  the  same  length,  one  of 
which  is  closed  at  the  top,  is  an  octave.     Explain  why. 


APPENDIX  A. 

Mathematical  Formulas. 

TT  =  3.14159. 

Circumference  of  circle  —  K  D. 

Area  of  a  circle  =  TT  R2. 

Surface  of  a  sphere  =  4  TT  R2  =  n  D2. 

Volume  of  a  sphere  f  TT  R3  =  |  TT  D3. 

APPENDIX  B. 

Soldering. — The  teacher  or  pupil  will  often  find  it  very  con- 
venient to  be  able  to  solder  together  two  pieces  of  metal.  The  pro- 
cess here  described  is  very  simple  and  will  answer  in  most  cases. 
A  bit  of  soft  solder,  the  size  of  a  hazlenut,  may  be  had  gratis  of  any 
good  natured  tinsmith  or  plumber.  Cut  this  into  bits  the  size  of  a 
grain  of  wheat  and  keep  on  hand.  Dissolve  a  teaspoonful  of  zinc 
chloride  (muriate  of  zinc)  in  water  and  bottle  it.  It  may  be  labelled 
"soldering  fluid."  If  you  have  not  a  spirit-lamp  obtain  one,  or 
make  one.  A  small  bottle  (such  as  those  in  which  school-inks  are 
commonly  sold)  will  answer  your  purpose.  Get  a  loosely  fitting  cork 
and  through  it  pass  a  metal  tube  about  an  inch  long  and  the  size  of 
an  ordinary  lead  pencil.  Through  this  tube,  pass  «,  bit  of  candle 
wicking.  Fill  the  bottle  with  alcohol,  insert  the  cork,  with  tube 
and  wick,  and  in  a  few  minutes  the  lamp  is  ready.  Having  now 
the  necessary  materials  you  are  ready  for  work.  For  example,  sup- 
pose that  you  are  to  solder  a  bit  of  wire  to  a  piece  of  tinned  ware. 
If  the  wire  be  rusty,  scrape  or  file  it  clean  at  the  place  of  joining. 
By  pincers  or  in  any  convenient  way  hold  the  wire  and  tin  together. 
Put  a  few  drops  of  " soldering  fluid"  on  the  joint,  hold  the  tin  in 
the  flame  so  that  the  wire  shall  be  on  the  upper  side,  place  a  bit  of 
solder  on  the  joint  and  hold  in  position  until  the  solder  melts.  Re- 
move from  the  flame  holding  the  tin  and  wire  together  until  the 
solder  has  cooled.  The  work  is  done.  If  you  have  a  "soldering- 
iron,"  you  can  do  a  wider  range  of  work,  as  many  pieces  of  work 
cannot  be  held  in  the  lamp  flame. 


APPENDIX. 


443 


APPENDIX  0. 

Centrifugal  Force.— (See  §  77.)  Let  a  body  placed  at  A  re- 
ceive  an  impulse  which  would  push  it  in  one  second  to  D,  while 
it  is  acted  upon  by  a  second 
force  which  in  the  same  time 
would  draw  it  to  B.  Then 
(see  §  82)  it  will  move  through 
the  diagonal  AE.  Inertia 
would  then  carry  it  in  the  line 
EF  but  the  centripetal  force 
draws  it  toward  H  and  it  de- 
scribes a  second  diagonal  EG. 
But  the  action  of  the  cen- 
tripetal force  is  continuous 
instead  of  intermittent  as  we 
have  described  it.  Conse- 
quently, the  moving  body  will 
change  its  direction  at  every 
point  and  describe  a  curve. 
Since  ED,  the  distance  that  FIG.  345. 

the  body  would  have  receded 

in  one  unit  of  time,  is  equal  to  AB,  the  two  central  forces  are  equal 
and  the  curve  is  a  circle.  If  the  arc  AE.be  sufficiently  small  it  will 
not  sensibly  differ  from  the  diagonal  AE.  Since  the  triangles 
ABE  and  AEO  are  similar,  we  have 


AB  :  AE  ::  AE  :  AO. 


AB  = 


But  AB  represents  the  centripetal  force  and  its  equal  the  cen- 
trifugal, while  AE  represents  the  velocity,  and  AO  the  diameter 
or  twice  the  radius. 


Hence  the  formula  :  C.  F.  =  — 
2r 


(1.) 


In  this  formula,  C.  F.  represents  a  line,  the  distance  over  which 
the  centrifugal  force  will  move  the  given  body.  If  we  wish  to 
measure  this  force  by  pounds  or  weight,  we  must  compare  it  with 
the  force  of  gravity,  which  is  the  cause  of  weight.  A  body ,  whose 
weight  may  be  represented  by  w,  will  fall,  when  acted  upon  by 
gravity  alone,  16.08  feet  in  one  second.  Hence : 


10  :  C.  F.  .: :  16.08  :  — . 


r  P  - 
' 


wv* 
32.16r 


(2-) 


444  APPENDIX. 


Letting  t  represent  the  number  of  seconds  required  to  make  one 
revolution, 

— — 
v 

Remembering  that  TT  =  3.14159,  we  have 


Representing  the  number  of  revolutions  per  second  by  n,  we  have 
v  =  2  irm.  /.     C.  F.  =  1.2275  wrn*. 

Caution. — In  using  these  last  two  formulas  for  "centrifugal 
force,"  care  must  be  taken  that  radius  be  expressed  in  feet. 

APPENDIX  D. 

Prince  Rupert  Drops. — A  neat  illustration  of  the  trans- 
mission of  pressure  by  liquids  (§  216),  may  be  given  by  filling  a 
small  bottle  with  water,  holding  a  Prince  Rupert  drop  in  its  mouth, 
and  breaking  off  the  tapering  end.  The  whole  "  drop  "  will  be  in- 
stantly shattered  and  the  force  of  the  concussion  transmitted  in 
every  direction  to  the  bottle  which  will  be  thus  broken.  These 
"drops"  are  not  expensive  ;  they  may  be  obtained  from  James  W, 
Queen  &  Co.,  924  Chestnut  street,  Philadelphia. 

APPENDIX  E. 

Difference  between  Theory  and  Practice.— The  re- 
sults mentioned  in  §  256  are  never  fully  attained  in  practice.  Only 
the  particles  near  the  centre  of  the  jet  attain  the  theoretical  velocity. 
Further  than  this,  if  we  carefully  examine  the  stream  we  shall 
notice  that  at  a  little  distance  from  the  orifice  the  stream  is  not  more 
than  two-thirds  or  three-fourths  the  size  of  the  orifice.  This  is  due 
to  the  fact  that  the  liquid  particles  come  from  all  sides  of  the 
opening,  and  thus  flow  in  different  directions,  forming  cross  currents, 
which  may  be  seen  if  there  are  solid  particles  floating  in  the  water. 
These  cross  currents  impede  the  free  flow  and  diminish  the  volume 
of  liquid  discharged.  Short  cylindrical  or  funnel-shaped  tubes  in- 
crease the  actual  flow.  In  a  cylindrical  tube,  this  narrowing  of  the 
jet  could  not  take  place  without  forming  a  vacuum  around  the  nar- 
row neck  (called  the  vena  contracta}.  The  pressure  of  the  atmos- 
phere, tending  to  prevent  this  formation  of  such  a  vacuum,  increases 


APPENDIX.  445 

the  velocity  and  the  volume  of  the  discharge.  The  funnel-shaped 
tube  prevents  the  formation  of  cross  currents  by  leading  the  liquid 
more  gradually  to  the  point  of  exit. 

APPENDIX  F. 

Barker's  Mill. — A  working  model  of  this  apparatus  (§  264) 
may  be  easily  made  by  any  wide-awake  pupil.  Select  a  long,  sound 
lamp-chimney  and  a  fine-grained  cork  that  snugly  fits  the  lower  end. 
Take  a  piece  of  glass  tubing,  the  size  of  a  lead  pencil,  heat  it  intensely 
in  an  alcohol  or  gas  flame  until  you  melt  off  a  piece  a  little  shorter 
than  the  lamp  chimney.  By  reheating  the  end  thus  closed  by 
fusion,  you  may  give  it  a  neat,  rounded  finish.  Prepare  four  pieces 
of  glass  tubing,  each  12  cm,  long.  These  pieces  would  better  be 
made  of  tubing  smaller  than  that  just  used.  To  cut  the  tube  to  the 
desired  length,  scratch  the  glass  at  the  proper  point  with  a  tri- 
angular file,  hold  the  tube  in  both  hands,  one  hand  on  each  side  of 
the  mark  just  made,  knuckles  uppermost  and  thumb-nails  touching 
each  other  at  a  point  on  the  tube  directly  opposite  the  file-scratch, 
push  with  the  thumbs  and  at  the  same  time  pull  with  the  fingers. 
The  tube  will  break  squarely  off.  Smooth  the  sharp  edges  by  soft- 
ening in  the  alcohol  flame.  Bend  each  of  these  four  pieces  at  right 
angles,  2  cm.  from  each  end,  in  such  a  way  that  one  of  the  short 
arms  may  be  in  a  horizontal  plane  while  the  other  short  arm  of  the 
same  piece  is  in  a  vertical  plane.  The  tubes  may  be  easily  bent 
when  heated  red-hot  at  the  proper  points  in  the  alcohol  or  gas  flame. 
See  that  the  four  pieces  are  bent  alike.  In  the  middle  of  the  cork, 
cut  a  neat  hole  a  little  smaller  than  the  tube  first  prepared.  Near 
the  edge  of  the  cork,  at  equal  distances,  cut  four  holes  a  little 
smaller  than  the  four  pieces  of  bent  tubing.  Push  the  open  end  of 
the  straight  tube  through  the  middle  hole.  From  the  other  side  of 
the  cork,  enter  one  end  of  each  bent  tube  into  one  of  the  four  holes. 
Place  the  cork  with  its  five  tubes  into  the  end  of  the  chimney,  see- 
ing to  it  that  the  straight  tube  lies  along  the  axis  of  the  chimney, 
i.  e.,  is  parallel  with  the  sides  of  the  chimney.  The  closed  end  of 
the  central  tube  should  be  near  the  open  end  of  the  lamp  chimney. 
In  pushing  the  tubes  into  the  cork,  grasp  the  tube  (previously  dip- 
ped in  soap  and  water)  near  the  cork,  and  screw  it  in  with  a  slow, 
rotary  onward  motion.  See  that  the  bent  tubes  are  at  right-angles  to 
each  other,  like  those  shown  in  Fig.  91.  For  a  support,  take  a  piece 
of  stout  wire,  small  enough  to  turn  easily  in  the  central  tube,  and  a 
little  longer  than  the  chimney.  Place  one  end  in  the  middle  of  a  tin 
pepper-box  and  fill  the  box  with  melted  lead.  This  makes  a  firm 


446  APPENDIX. 

base-  File  the  other  end  of  the  wire  to  a  sharp  point.  For  a  few 
cents,  such  a  wire  with  an  iron  base  may  be  had  ready  made  at  the 
stationer's.  Pass  the  straight  tube  of  the  apparatus  over  this  wire 
until  the  closed  tube  rests  upon  the  sharpened  point.  The  chimney 
with  its  four  horizontal  arms  is  now  delicately  suspended,  free  to 
revolve  in  stable  equilibrium.  Place  the  apparatus  in  the  middle  of 
a  tub  and  pour  water  into  the  open  end  of  the  chimney.  Tour 
wheel  will  work  as  well  as  Edgerton's  or  Ritchie's.  The  satisfac- 
tion of  seeing  the  machine  work  and  knowing  that  you  made  it  will 
amply  repay  the  cost,  leaving  the  instruction  and  added  skill  for 
clear  profit. 

APPENDIX  G. 

Balloons.— (See  §272.)  A  little  thought  concerning  the  full 
meaning  of  Archimedes'  Principle  will  show  that  if  a  body  weighs 
less  than  its  own  bulk  of  air  it  will  rise  in  the  air.  Thus  soap- 
bubbles  filled  with  hydrogen  or  other  light  gas  will  ascend.  If  the 
bubble  be  made  from  hot  water  and  filled  with  warm  air  it  will 
rise ;  if  it  be  made  from  cold  water  and  filled  with  cold  air  it  will 
fall.  (Explain  why.)  The  same  principle  applies  to  balloons.  A 
balloon  will  support  a  weight  equal  to  the  difference  between  the  weight 
of  the  balloon  with  the  contained  gas  and  the  weight  of  the  air  dis- 
placed. A  liter  of  hydrogen  weighs  0.0896  g. ;  a  liter  of  coal  gas, 
from  0.45  g.  to  0.85  g. ;  a  liter  of  air  heated  to  200°  Centigrade,  about 
0.8  g.  During  the  siege  of  Paris  in  1870,  the  Parisians  communi- 
cated with  the  outer  world  by  means  of  balloons  about  50  feet  in 
diameter,  having  a  capacity  of  about  70,600  cu.  ft.  These  balloons 
with  net  and  car  weighed  about  1000  pounds  each  and  had  a  carry- 
ing ability  of  about  2000  pounds.  Balloons  have  been  made  about 
100  feet  in  diameter,  having  a  capacity  of  about  half  a  million  cubic 
feet.  In  1861,  an  ascent  was  made  to  a  height  of  seven  miles. 

APPENDIX  H. 

Atmospheric  Pressure.— (See  §  275.)  Into  a  bent  glass 
tube,  ACS,  pour  mercury  to  a  height  of  about  20  inches,  or  50  cm. 
The  mercury  will,  of  course,  stand  at  exactly  the  same  level,  ac,  in 
the  two  branches.  If  equal  pressures  of  any  kind  be  exerted  upon 
the  surfaces  of  the  mercury  at  a  and  c,  this  level  will  not  be  dis- 
turbed, while  any  difference  of  pressure  would  be  promptly  shown 
by  the  movement  of  the  mercury  and  a  consequent  difference  in. 
the  heights  of  the  two  mercury  columns.  The  atmosphere  pi 


APPENDIX. 


447 


upon  both  mercurial  surfaces,  at  a  and  c,  but  it  presses  upon  them 
equally,  and  therefore  does  not  change  the  common  level.  Into  the 
arm  A,  push  an  air-tight  piston,  p,  which  has  a  valve 
opening  upward  but  not  downward.  As  this  piston 
is  pushed  downward,  the  air  in  A  escapes  through 
this  valve,  and  p  finally  rests  upon  the  surface  of  the  A 
mercury  at  a.  When  the  piston  p  is  subsequently 
lifted  to  A,  the  atmospheric  pressure  is  wholly  re- 
moved from  the  surface  of  the  mercury  in  that  arm 
of  the  tube,  while  it  acts  with  unchanged  intensity 
upon  the  surface  at  c.  The  consequence  is  that  the 
mercury  follows  the  piston  until  there  is  a  difference 
of  about  760  mm.  or  30  inches  between  the  levels  of 
the  mercury  in  the  two  arms  of  the  tube.  If  the 
tube  have  a  sectional  area  of  one  square  inch,  the 
mercury  thus  supported  would  weigh  about  15 
pounds,  and  would  exactly  equal  the  weight  of  an 
air  column  of  the  same  sectional  area,  reaching  from 
the  apparatus  to  the  upper  surface  of  the  atmos- 
phere. 

APPENDIX  I. 


Magnetic  Needles. — Magnets  may  be  made 
for  the  experiments  described  in  §  306  by  magnet-      FIG.  346. 
izing  three  stout  knitting-needles  (see  §  320).     They 
may  be  suspended  by  means  of  a  triangular  piece  of  stiff  writing- 
paper.    Pass  the  needle  through  the  paper  near  the  lower  corners  ; 
at  the  other  corner  affix  by  wax  the  end  of  a  horse-hair,  which  will 
exert  no  torsion.    The  poles  may  be  indicated  by  little  bits  of  red 
and  of  white  paper,  fastened  by  means  of  wax  to  the  ends  of  the 
needles. 

APPENDIX  J. 

Dipping-Needle. — A  dipping-needle  may  easily  be  made  by 
thrusting  a  knitting-needle  through  a  cork  so  that  the  cork  shall  be 
at  the  middle  of  the  needle.  Thrust  through  the  cork,  at  right 
angles  to  the  knitting-needle,  half  a  knitting-needle,  or  a  sewing- 
needle,  for  an  axis.  Support  the  ends  of  the  axis  upon  the  edges 
of  two  glass  goblets  or  other  convenient  objects  (see  Fig.  131). 
Push  the  knitting-needle  through  the  cork  so  that  it  will  balance 
upon  the  axis  like  a  scale-beam.  Magnetize  the  knitting-needle 
and  notice  the  dip.  (See  §  314  [a].) 


4:4:8  APPENDIX. 


APPENDIX  K. 

Electroscopes.— (See  §  332.)  For  directions  for  making 
simple  and  efficient  electroscopes,  see  Tyndall's  ''Lessons  on  Elec- 
tricity," §  7.  For  an  electroscope  for  the  electrophorus  (§  343),  pro- 
vide a  bit  of  wire  about  8  em.  long,  and  bend  it  at  right  angles  about 
1  cm.  from  each  end.  Solder  one  of  the  bent  arms  of  the  wire  (see 
Appendix  B)  to  the  upper  side  of  the  tinned  plate,  near  its  edge,  in 
such  a  way  that  the  central  part  of  the  wire  shall  be  vertical.  Cut  a 
strip  of  gold-leaf  (or  Dutch  metal)  about  8cm.  long  and  8mm.  wide. 
Moisten  the  sides  of  the  free  horizontal  wire  arm  with  a  little 
mucilage,  place  the  middle  of  the  gold-leaf  strip  over  the  top  of  the 
arm,  and  bring  the  ends  of  the  leaf  down  to  a  vertical  position, 
touching  each  other.  The  mucilage  will  hold  the  leaf  to  the  wire. 
When  the  wire  support  and  gold-leaves  are  electrified,  the  latter 
will  diverge.  When  the  apparatus  is  not  in  use,  this  electroscope 
may  be  protected  by  inverting  a  tumbler  or  beaker  glass  over  it. 


APPENDIX  L. 

Thermo-Electricity. — (See  §  412.)  The  frame  may  be  sim- 
plified by  bending  a  strip  of  copper  twice  at  right  angles  to  make 
the  top,  bottom  and  one  end  of  the  frame,  the  other  end  being  a 
cylinder  of  bismuth.  But  the  form  shown  in  Fig.  207  is  prefer- 
able, as  the  same  junction  may  be  heated  by  the  lamp  below  or 
chilled  by  laying  a  piece  of  ice  on  the  upper  side. 

APPENDIX  M. 

The  Telephone.— (See  §  446.)  The  theory  that  the  diaphragm 
of  the  receiving  telephone  is  made  to  vibrate  to  and  fro  by  the  vary- 
ing intensity  of  the  magnetic  attraction  of  the  iron  core  has  lately 
been  questioned.  Many  experiments  go  to  show  that  the  variations 
in  the  magnetic  intensity  of  the  iron  core  are  too  feeble  to  produce 
such  mechanical  effects.  It  also  appears  that  paper  and  other  sub- 
stances may  replace  the  iron  of  the  diaphragm  in  the  receiving  tele- 
phone, without  destroying  the  sounds,  and  that  the  diaphragm  may 
even  be  removed  and  the  sounds  still  produced  and  transmitted  to 
the  ear.  These  facts  are  believed  to  show  that  the  reproduced  sound 
is  due  to  movements  of  the  molecules  of  the  iron  core,  such  molecular 
motions  being  due  to  the  electric  currents  from  the  "  transmitter  "  (or 


APPENDIX.  449 

telephone  spoken  to),  and  that  the  diaphragm  is  valuable  for  the 
purposes  of  strengthening  the  sound  (§  444,  b)  and  transmitting  it  to 
the  ear  of  the  listener.  The  scientific  paper,  Nature,  says  that  care- 
ful investigation  leads  to  the  conclusion  that,  at  the  sending  station, 
the  evidence  of  molecular  action,  though  suggestive,  is  by  no  means 
conclusive,  whereas,  at  the  receiving  station,  the  existence  of  molec- 
ular as  well  as  mechanical  action  amounts  to  demonstration  and  is 
shown  to  be  considerable  in  amount. 

APPENDIX  N. 

The  Phonograph.— (See  §  447.)    The  appearance  of  this  in- 
strument is  shown  in  the  accompanying  cut,  in  which  F  represents 


FIG.  447- 

the  mouthpiece ;  C,  the  cylinder  covered  with  tin-foil ;  E,  the  axis 
with  a  thread  working  in  A,  one  of  the  two  supports.  The  mouth- 
piece, with  its  diaphragm  and  style,  may  be  moved  toward  the 
cylinder  or  from  it,  by  means  of  the  supporting  lever,  HG,  which 
turns  in  a  horizontal  plane  about  the  pin  /. 


APPENDIX  0. 

Differential  Thermometer.— (See  §  482.)  Prepare  two 
boards,  each  5x7  inches  and  an  inch  thick.  Place  them  upon  end 
parallel  to  each  other,  7  inches  apart.  Connect  the  boards  by 
nailing  to  their  tops  two  thin  strips,  each  an  inch  wide  and  9  inches 
long.  The  strips  will  be  3  inches  apart.  This  is  our  stand.  For 
the  two  bulbs  use  two  tin  oyster  cans  with  flat  sides.  To  the  centre 
of  one  end  of  each  solder  a  tin  tube,  1|  inches  long  and  f  of  an 


450  APPENDIX. 

inch  in  diameter.  Take  a  30-inch  piece  of  glass  tubing  that  will 
slide  easily  within  the  tin  tubes.  Bend  it  at  right  angles,  12  inches 
from  each  end,  like  the  tube  shown  in  Fig.  240.  Color  a  little 
alcohol  with  red  aniline,  and  pour  into  the  bent  tube  enough  to  fill 
an  inch  or  two  above  each  bend.  Over  each  arm  of  the  bent  tube 
pass  an  inch  of  snugly-fitting  rubber-tubing,  and  slide  it  down 
about  8  inches.  Pass  the  arms  of  the  glass  tube  up  through  the 
tin  tubes  of  the  inverted  cans  as  far  as  they  will  go.  Slide  the 
rubber-tubing  upward  to  make  air-tight  joints  between  the  glass 
and  the  tin  tubes.  Place  the  cans  upon  the  horizontal  strips  of  the 
frame  already  made,  allowing  the  glass  tube  to  hang  between  the 
boards.  The  level  of  the  liquid  in  either  arm  may  be  marked  by  a 
thread  or  rubber  band  that  may  be  moved  up  or  down. 


NUMBERS   REFER   TO    PARAGRAPHS 


Aberration,  Chromatic,  646. 

Spherical,  633. 
Absolute  pitch  of  sound,  459. 

"         unit  of  force,  68. 
Absorption  and  radiation  of  heat  and 

light,  654,  655. 
Absorption  of  heat,  553, 
Achromatic  lens,  647. 
Acoustic  tubes,  433. 
Actinic  spectrum,  651,  652. 
Adhesion  defined,  46. 
Aerial  ocean,  271. 
Agriform  body  defined,  57,  61. 
Affinity,  Chemical,  568. 
Air-chamber,  297. 
Air-pump,  288-293. 
Air,  weight  of,  272. 
Amalgamating  zincs,  386. 
Amplitude  of  vibration,  140,  419,  431. 
Aneroid  barometer,  280. 
Angle  of  incidence,  97. 
Apparent  direction  of  bodies,  594. 
Archimedes'  principle,  238,  239. 
Armatures  for  magnets,  321. 
Artificial  magnet,  303. 
Ascending  bodies,  132. 
Astatic  needle,  314. 
Astronomical  telescope,  66 1. 
Athermanous,  552. 
Atmospheric  electricity,  350. 

pressure,    273,    275,    277, 

App.  H. 
Atom  defined,  6. 
Attraction,  Capillary,  235. 

"          Electric,  323. 

"          Forms  of,  7. 

"          Magnetic,  305,  306. 
Attwood,  122. 

B 

Balance,  175. 
Balance,  False,  176. 


Balloons,  App.  G.  (.     , 

Barker's  mill,  264,  App.  F. 
Barometer,  274,  278,  279,  280. 
Baroscope,  281. 
Battery,  Leyden,  357. 

u        Voltaic,  379-385. 
Beam  of  light,  583. 
Beats,  452,  453. 
Beaume's  hydrometer,  252. 
Bellows,  Hydrostatic,  222. 
Bent  levers,  173. 

Bi-chromate  of  potassium  battery,  383^ 
Boiling-point,  479,  501-510. 
Breast  wheel,  262. 
Brittleness  defined,  49. 
Broken  magnets,  307. 
Bunsen's  air-pump,  291. 

"        battery,  385. 

C 

Calorific  powers,  569. 
Calorimeter,  531. 

Camera,  The  photographer's,  656. 
Capillary  attraction,  235. 

phenomena,  236. 
Cathetal  prism,  621  (c). 
Centrifugal  force,  74,  App.  C. 
C.  G.  S.  units,  69,  154. 
Changes,  Chemical,  n. 

Physical,  10. 

of  condition  of  matter,  59. 
Characteristic  properties,  19,  21. 
Charging  by  induction,  339,  340. 
Chemical  affinity,  568. 

changes,  n. 

"         effects  of  electricity,  368,  397. 
"         properties,  15. 
Chromatic  aberration,  646. 
Chromatics,  634. 
Clarionet,  471. 
Clouds,  Electrified,  361. 
Cohesion  defined,  46. 
Coincident  waves,  448. 


452 


INDEX. 


Numbers  refer  to  Paragraphs. 


Color  of  bodies,  640. 
Communicating  vessels,  234. 
Compass,  314. 

Compensating  pendulum,  149. 
Composition  of  forces,  80,  88. 
Compound  machines,  211. 
Compressibility  defined,  43. 
Concave  lens,  622,  626,  632. 
Condensation  of  electricity,  351. 
Condensers,  292,  352. 
Conditions  of  matter,  53. 

44  "       Changes  of,  59. 

Conduction  of  electricity,  333. 

"  heat,  538. 

Conjugate  foci,  602,  625,  626. 
Construction  for  images,  597,  605,608, 

628. 

Convection  of  heat,  541. 
Convertibility  of  energy,  159. 
Convex  lens,  622-625,  627-631. 
Critical  angle,  617. 
Culinary  paradox,  505. 
Curves,  Magnetic,  313. 
Cycloidal  pendulum,  144. 


Daniell's  battery,  381. 
Declination,  Magnetic,  319. 
Density,  Electric,  350. 
Diamagnetic  substances,  310. 
Diathermancy,  552. 
Dielectric  machine,  347,  348. 
Differential  thermometer,  482,  App.  M. 
Diffused  light,  592. 
Diffusion  of  heat,  537. 
Dip,  Magnetic,  318. 
Dipping  needle,  314,  318. 
Direction,  Line  of,  65,  114. 
Direction  of  bodies,  Apparent,  594. 
Discharger  for  electricity,  355,  371  (23). 
Dispersion  of  light,  636. 
Distillation,  511-513?       '  *  ^' 
Distribution  of  electricity,  358,  359. 
Divisibility  defined,  41. 
Divisions  of  matter,  3. 
Double  refraction,  673. 
Double  weighing,  177. 
Downward  pressure,  225,  226. 
Ductility  defined,  51. 
Duration  of  electric  spark,  364. 
Dynamics  defined,  63. 
Dyne  defined,  69. 


Ebullition,  501-510. 

Eccentric,  573. 

Echo,  442. 

Effects  of  electricity,  365-370,  388,  392, 

397,  402. 
Elasticity,  45. 

Electric  action,  Law  of,  329. 
41         attraction,  323. 

bells,  371  (i). 
u         bomb,  371  (20). 
"         circuit,  376. 
"        chime,  371  (2). 
44         condensers,  352. 
u         conductors,  333. 
u         current,  374,  375,  4°3-4°9- 
u         currents,  Induced,  403. 
u         density  or  tension,  350. 
"         effects,  365-37°.  388>  392*  397. 

402. 

"        experiments,  371. 
u         force,  325. 

44         fluids,  Theory  of,  335,  336. 
44         induction,  337-3*0. 
44         lamp,  389. 
light,  653. 

"         machines,  345-349- 
44         orrery,  371  (n). 
u         repulsion,  324. 
"         resistance,  378. 
"         spark,  364,  371  (24),  411. 
44         telegraph,  395. 
44         tension,  350. 
44        whirl,  371  (10). 
Electricity  and  energy,  372. 
44         Atmospheric,  360. 
44         Condensation  of,  351. 
"          Condenstrs  of,  352. 
•4          Distribution  of,  358,  359. 
44         Kinds  of,  326,  327,  328. 
44         Tests  for,  330,  331,  332. 
44         Thermo-,  412. 
44         Velocity  of,  364. 
44         Voltaic,  373. 
Electrics,  334. 
Electrodes,  377. 
Electrolysis,  397^  398. 
Electrolyte,  397. 
Electro-plating.  399. 
Electrophorus,  342,  343. 
Electroscope,  331,  332,  App.  K. 
Electrotyping,  400. 


INDEX. 


453 


Numbers  refer  to  Paragraphs. 


Endless  screw,  210. 

Energy  a  constant  quantity,  160. 

u       and  electricity,  372. 

44       Conservation  of,  675. 

"       Convertibility  of,  159,  516, 517. 

"       Correlation  of,  562,  676. 

'l       defined,  151. 

u       Formula  for,  157. 

u       Indestructibility  of,  162. 

"       Types  of,  158. 

"       Varieties  of,  674. 
Engine,  The  steam,  570. 
English  measures,  23. 
Equilibrant,  86. 
Equilibrium;  110-113. 
Equilibrium  of  liquids,  233. 
Erg  defined,  154. 
Evaporation,  499,  500. 
Expansibility  defined,  44. 
Expansion  by  heat,  483-492. 
Extension  defined,  22. 
Eye,  The  human,  657. 


Fahrenheit's  hydrometer,  251. 

44  thermometer,  480. 

Falling  bodies,  119. 

u         "        Laws  of,  129. 
False  balance,  176. 
Fife,  471. 

Floating  bodies,  240. 
Flow  of  liquids,  254-259. 
Fluid  defined,  60,  61. 

"     displaced  by  immersed  solid,  237 
Flute,  471. 
Fly-wheel,  574. 
Focus  of  heat,  555,  556. 

light,  599, 601-603, 624-626. 
Focus  of  sound,  439. 
Foot-pound  defined,  153. 
Force,  Absolute  unit  of,  68. 
44       Constant,  118. 
44       Centrifugal,  74. 
u      defined,  64. 

Electric,  325. 
44      Elements  of  a,  65. 
Gravity  unit  of,  67. 
44       Kinetic  unit  of,  68. 
44      Measurement  of,  66. 

of  gravity  resolved,  199. 
44      pump,  297. 
Forces,  Composition  of,  80. 


Forces,  Graphic  representation  of,  81. 

44        Moments  of,  171. 

"        Parallelogram  of,  82. 

"        Parallelopiped  of,  90. 

44        Polygon  of,  89. 

"        Resolution  of,  91. 

44       Triangle  of,  87. 
Forms  of  attraction,  7. 

44          motion,  8. 

Formulas,  Mathematical,  App.  A. 
Fraunhofer's  lines,  638. 
Freezing  mixtures,  521. 

44        point,  478. 
Friction,  212-214. 

41        develops  heat,  564. 
Fundamental  tones,  460,  461. 

G 

Galileo,  121,  660. 
Galvanic  battery,  379-385. 

"        electricity,  373. 
Galvanometer,  391. 
Gas  defined,  58. 
Gases,  Specific  gravity  of,  248. 
44      Tension  of,  269,  282-287,  494. 
44      Type  of,  270. 
Geissler's  tubes,  371  (31). 
Governor,  574. 

Graduation  of  thermometers,  477. 
Gram  defined,  36. 

Graphic  representation  of  forces,  81. 
Gravitation  defined,  98. 
Gravitation,  Laws  of,  100. 
Gravity,  Centre  of,  107-110. 

44       defined,  102. 

44        Force  of,  resolved,  199. 

44       Increment  of,  127. 

*4        Specific,  241-253. 
Gravity  unit  of  force,  67. 
Grove's  battery,  384. 

II 

Hardness,  47. 
Head  of  liquid,  254. 
Heating  powers,  569. 
Heat,  Conduction  of,  538. 

44      Convection  of,  541. 

*      defined,  473. 

44      Diffusion  of,  537. 

44      from  friction,  564. 

44      from  percussion,  563. 

44      Latent,  518-530. 

44      Radiation  of,  542,  545. 


454 


Numbers  refer  to  Paragraphs. 


Heat,  Reflection  of,  554. 

u      Refraction  of,  556. 

"      Sensible,  516,  517. 

"      Specific,  531-536. 

14      units,  514. 
Heliostat,  page  376  (note). 
Holtz  electric  machine,  349. 
Horizontal  needle,  314. 
Horse-power  defined,  155. 
Human  eye,  657. 
Hydrokinetics,  254. 
Hydrometers,  249-252. 
Hydrostatic  bellows,  222. 
u  paradox,  229. 

"  press,  223. 

Hypothetical  theory,  309. 


Iceland  spar,  673. 

Images,  Construction  for,  597,  603,  605. 

"        Inverted,  585. 

"        Multiple,  598. 

u        Projection  of,  606 

"        Real,  604-607,  629,  630. 

"         Virtual,  595,  608,  610,  631,  632. 
Impenetrability  defined,  31. 
Incidence,  Angle  of,  97. 
Inclination,  Magnetic,  318. 
Inclined  plane,  198-204. 
Incompressibility  of  liquids,  215. 
Increment  of  velocity,  127. 
Indestructibility  of  energy,  162. 

"  matter,  37. 

Index  of  refraction,  613. 
Induced  electric  currents,  403. 
Induction,  Electric,  337-34°- 

"         Magnetic,  311,  312. 
Inertia  defined,  38. 
Intensity  of  light,  589.  ^ 

Intensity  of  sound,  431,  432. 
Interference  of  sound,  451.  / 
Intermittent  springs,  301. 
Internal  reflection  of  light,  616. 
Inverted  images,  585. 
Invisibility  of  light,  593. 


Joule's  equivalent,  566. 

K 

Kinetic  energy,  Formula  for,  157- 
u       unit  of  force,  63. 


Latent  heat,  518-530. 
Lateral  pressure,  230,  231. 
Lenses,  622. 
Leslie's  cube,  554,  558. 
Lever,  Classes  of,  169. 
"      Compound,  178. 
u      defined,  168. 
"       Laws  of,  170. 
Leyden  battery,  357. 
"       jar,  353-356. 
Lifting-pump,  294. 
Light  defined,  579. 
u     Diffused,  592. 
"     Dispersion  of,  636. 
Electric,  653. 
Invisibility  of,  593. 
Motion  of,  584. 
Polarization  of,  667. 
Reflection  of,  590. 
Refraction  of,  612. 
Synthesis  of,  639. 
"     Velocity  of,  588. 
Lightning,  362. 
Lightning-rods,  363. 
Liquid  defined,  55,  6x. 

u      rest,  Conditions  of,  232. 
Liquids,  Equilibrium  of,  233. 

"       flowing   through   pipes,    257, 

259- 

u       in  communicating  vessels,  234, 

u        Incompressibility  of,  215. 

"       Spouting,  254-256. 
Liter  defined,  29. 
Loudness  of  sound,  431. 
Luminous  bodies,  580. 

"          effects  of  electricity,  366. 

u          spectrum,  649,  652. 

M 

Machine  cannot  create  energy,  164, 165. 

"        defined,  163. 

"        Laws  of, -167. 
Uses  of,  166. 
Machines,  Compound,  211. 

u          Electric,  345-349- 
Magic  lantern,  664. 
Magnet,  Artificial,  303, 

"       Natural,  302. 
Magnetic  curves,  313. 

il         declination  or  variation,  319. 

"         effects  of  electricity,  367,  392. 


INDEX. 


455 


Numbers  refer  to  Paragraphs. 


Magnetic  force,  Distribution  of,  304. 

44         inclination  or  dip,  318. 

44         induction,  311,  312,  338. 

14         needles,  314,  App.  I,  J. 

41         poles,  304,  306,  317. 

14         substances,  310. 
Magnetism,  Residual,  393. 

44  Terrestrial,  315,  316. 

44  Theory  of,  308,  336. 

Magnetization,  320,  394. 
Magnets,  Broken,  307. 

44         Electro-,  393. 

"         How  made,  320,  394. 
Magnifying-glass,  658. 
Malleability  defined,  50. 
Malus's  polariscope,  672. 
Marcet's  globe,  507. 
Mariner's  compass,  314. 
Mariotte,  284,  285. 
Mass  defined,  4,  6. 
Mathematical  formulas,  App.  A. 
Matter,  Conditions  of,  53. 
44       defined,  2, 
'4       Divisions  of,  3. 
"       Properties  of,  13. 
Measures,  23-30,  34-36. 
Mechanical  effects  of  electricity,  369. 

"  equivalent  of  heat,  566. 

Meter  defined,  25. 
Metric  measures,  24-30,  35,  36. 
Microscope,  658,  659. 
Mirrors,  Concave,  599-609. 

44       Convex,  610. 

Parabolic,  601  (a). 

44        Plane.  595-598. 
Mobility  defined,  40. 
Molecules  defined,  5,  6. 
Moment  offerees,  171, 172. 
Momentum  defined,  70. 
Motion,  Forms  of,  8. 

44        Newton's  laws  of,  72,  73,  78, 93. 

44       of  the  pendulum,  139. 

"       Reflected,  96,  97. 

44       Resultant,  79. 
Multiple  images,  598. 
Music,  429,  430. 
Musical  instruments,  465-471. 

scale,  456,  457. 
44       strings,  454,  455. 


Natural  magnet,  302. 


Natural  Philosophy  defined,  12. 

Needles,  Magnetic,  314. 

Newton's  laws  of  motion,  72,  73,  78, 93 

Nicholson's  hydrometer,  250. 

Nodal  points  or  nodes,  460. 

Noise,  428. 

Non-luminous  bodies,  580. 

O 

Ocean,  The  aerial,  271. 
Opaque  bodies,  581. 
Opera-glass,  660. 
Optical  centre,  623. 
Organ  pipes,  469. 
Oscillation,  Centre  of,  141. 

44          of  pendulum,  140. 
Overshot  wheel,  261. 
Overtones,  460,  462,  463. 

P 

Papin's  digester,  506. 
Paradox,  Hydrostatic,  229. 
Parallelogram  of  forces,  82. 
Parallelepiped  of  forces,  90. 
Pascal,  217,  218,  221,  276. 
Pencil  of  light,  583. 
Pendulum,  Compensation,  149. 

Compound,  138. 

Cycloidal,  144. 

Laws  of,  143,  145,  146. 

Motion  of  the,  139. 

Real  length  of,  142. 

Simple,  137. 

The  second's,  147. 
44          Uses  of,  148. 
Percussion  develops  heat,  563. 
Philosophy,  Natural,  defined,  12,  162. 
Phonograph,  447. 
Photographer's  camera,  656. 
Physical  change,  10. 

44         properties,  14,  15. 
"        science,  9. 
Physics  defined,  12,  162. 
Physiological  effects  of  electricity,  370, 

402. 

Pipes,  Musical,  466-471. 
Pitch  of  sound,  434-437. 

44        Absolute,  459, 
Plane,  Inclined,  198-204. 
Plate  electric  machine,  345,  346. 
Plating,  Electro-,  399. 
Pneumatics  defined,  268. 
Pointed  conductors  of  electricity,  344. 


450 


INDEX. 


Numbers  refer  to  Paragraphs. 


Polariscope,  672. 
Polarization,  Electric,  341. 

"  of  light,  667-673. 

Poles,  Magnetic,  304,  306,  317. 
Polygon  of  forces,  89. 
Porosity  defined,  42. 
Porte-lumiere,  page  376  (note). 
Potassium  bi-chromate  battery,  383. 
Press,  Hydrostatic,  223. 
Pressure,  Atmospheric,  273,  275,  277. 
"         Downward,  225,  226. 
u         Lateral,  230,  231. 
"         Transmission  of,  by  liquids, 

216. 

"         Upward,  227,  228. 
Prince  Rupert  drops,  App.  D. 
Principal  axis,  599-623. 

"        focus,  599,  601,  624. 
Prisms,  62 1. 
Projectiles,  133. 

Path  of,  135. 
"  Time  of,  136. 

Proof-plane,  340,  358. 
Propagation  of  sound,  422. 
Properties,  Characteristic,  19,  21. 
u          Chemical,  15. 
"          of  matter,  13. 
"  Physical,  14,  15. 

"          Universal,  18,  20. 
Pulley,  192, 197. 
Pump,  Air,  288,  293. 
il      Force,  296,  297. 
"      Lifting,  294. 

Q, 

Quality  of  sound,  464. 

R 

Radiation  and  absorption  of  heat  and 

light,  654,  655. 

Radiation  of  sound,  542,  545. 
Rainbow,  641-645. 
Random,  134. 
Range,  134. 
Rays  of  light,  582. 
Reaction,  72,  93,  94,  95. 
Reed  pipes,  470. 
Reflected  motion,  96,  97. 
Reflecting  telescope,  662. 
Reflection  of  heat,  554. 
light,  590. 

"  sound,  440. 

"         Total  internal,  616. 


Refracting  telescope,  661. 
Refraction,  Double,  673. 

"  of  heat,  556. 

Index  of,  613. 

"  of  light,  612. 

"  "   sound,  438. 

Refractors,  Kinds  of,  619, 
Reinforcement  of  sound,  449. 
Repulsion,  Electric,  324. 
Resistance,  Electric,  378. 
Resolution  offerees,  91,  199. 
Resonance,  450. 
Resultant  motion,  79,  85. 
Rivers,  Flow  of,  258. 
Ruhmkorff's  coil,  410. 

S 

Safety-valve,  575. 
Scale,  Musical,  456,  457. 
Science  defined,  i. 

"       Physical,  9. 
Screw  defined,  208. 

"     Endless,  210. 

"      Law  of,  209. 
Secondary  axis,  599,  623. 
"         foci,  624  (3). 
Selective  absorption,  553. 
Sensible  heat,  516. 
Shadows,  586. 
Siphon,  298-300. 
Smee's  battery,  382. 
Solar  spectrum,  635. 
Soldering,  App.  B. 
Solid  defined,  54,  6t. 
Sonorous  tubes,  466. 
Sound  beats,  452,  453. 

"      Cause  of,  421. 

"      defined,  415. 

"      Focus  of,  439. 

"      Interference  of,  451. 

"      media,  424. 

"      Propagation  of,  422. 

"      Quality  of,  464. 

"      Reflection  of,  440. 

"      Refraction  of,  438. 

"      Reinforcement  of,  449, 

u      Velocity  of,  425-427. 

"      waves,  423. 
Sounding-board,  444. 
Spark,  Elec  ric,  364>  371  (24)« 
Speaking-tubes,  433. 
Specific  gravity  defined,  241. 


INDEX. 


45? 


Numbers  refer  to  Paragraphs. 


Specific  gravity  for  gases,  248. 

u  "         u  liquids,  242, 246. 

u  "         "  solids,  242-245. 

"        heat,  531-536. 
Spectroscope,  638  (b). 
Spectrum  635,  637,  648-653. 
Spherical  aberration,  633. 
Spouting  liquids,  254-256. 
Sprengel's  air-pump,  290. 
Springs,  Intermittent,  301. 
Stability,  116. 
Steam,  508,  529. 
Steam-engine,  570. 
Stereoscope,  665,  666. 
Strings,  Musical,  454,  455. 
Successive  induction,  340. 
Surveyor's  compass,  314. 
Sympathetic  vibrations,  443,  560. 
Synthesis  of  light,  639. 


Tantalus's  cup,  301. 
Telegraph,  395. 
Telephone,  408,  409,  445,  446. 
Telescope,  660-663. 
Temperature,  474,  494. 
Tenacity,  48. 
Tension,  Electric,  350. 
Tension  of  gases,  269,  282-287. 
Terrestrial  magnetism,  315,  316. 

M          telescope,  663. 
Tests  for  electricity,  330,  331,  332. 
Theory,  Hypothetical,  309. 

"       of  electricity,  335. 
magnetism,  308. 
Thermal  effects  of  electricity,  365,  387. 

"        spectrum,  650,  652. 

u        units,  514. 
Thermodynamics,  561. 

"  First  law  of,  565. 

Thermo-electricity,  412,  App.  L. 
Thermo-electric  pile,  414. 
Thermometers,  476-482. 
Thermometric  readings,  481. 

"  scales,  480. 

Timbre,  464. 

Tones,  Fundamental,  460,  461. 
Torricelli,  274. 

Total  internal  reflection,  616. 
Tourmaline  tongs,  670. 
Transferrer,  292 
Translucent  bodies,  581. 
Transmission  of  pressure  by  Iiquids,2i6. 


Transparent  bodies,  581. 
Triangle  offerees,  87. 
Tubes,  Acoustic,  433. 
u      Sonorous,  466. 
Turbine  wheel,  265. 

U 

Undershot  wheel,  263. 

Undulations,  416. 

Unit  of  heat,  514. 

-     "       work,  153,  154. 

Universal  properties,  18,  20. 

Upward  pressure,  227,  228. 

V 

Vapor  defined,  58. 
Variation,  Magnetic,  319. 
Velocity,  Increment  of,  127. 
"         of  electricity,  364. 
"  light,  588. 

Vertical  needle,  314,  318. 
Vibration  of  pendulum,  140. 
Vibrations,  Sympathetic,  443,  56*. 
Visual  angle,  587. 
Voltaic  arc,  389. 

"       battery,  379-385. 

u       electricity,  373. 
Volta's  pistol,-37i  (35). 

W 

Water,  Expansion  of,  488,  489. 

u       power,  260. 

"       Specific  heat  of,  536. 

"       wheels,  261-264. 
Wave  length,  418,  420,  437. 

u     period,  417,  420,  436. 
Waves,  Coincident,  448. 
Wedge  defined,  205. 
Wedge,  Use  of,  206,  207. 
Weight  defined,  33,  103. 
Weight,  Law  of,  105. 
Wheel  and  axle,  Advantages  of,  180. 

"        "      "      defined,  179. 

"        "      "      Forms  of,  184. 

"        "      "      Formulas  for,  182. 

"      "      Law  of,  183. 
Wheels,  how  connected,  189. 
Wheels,  Water,  261-264. 
Wheel-work,  185-188. 
Work  defined,  150. 
Work,  Unit  of,  153. 


Zero  cf  temperature,  Absolute,  493. 
Zincs,  Amalgamating,  386. 


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460  pages.     By  ELROY 


Avertfs  Natural  Philosophy. 

M.  AVEBY,  A.  M. 

The  book  is  an  earnest  and  eminently  successful  attempt  to  present  the  facts 
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A  Manual  of  English  Literature.  By  HENRY  MORLEY, 
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Thoroughly  revised,  with  an  entire  rearrangement  of  matter, 
and  with  numerous  retrenchments  and  additions,  by  MOSES 
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